Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D283 |
| commutator, socle, cosocle | C22×C283 | C24 |
| Fitting | #123×C283 | C2 |
| hypercenter | #123 | D283 |
| hypocenter | C283 | #546 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17985392 | C2 | semidirect |
| 2. C2×D4×D283 | C2 | semidirect |
| 3. #22583596 | C2 | semidirect |
| 4. #22583595 | C2 | semidirect |
| 5. #22583588 | C2 | semidirect |
| 6. #22583585 | C2 | semidirect |
| 7. #22583583 | C2 | semidirect |
| 8. #22583582 | C2 | semidirect |
| 9. #22583580 | C2 | semidirect |
| 10. #22583580 | C2 | semidirect |
| 11. #22583572 | C2 | semidirect |
| 12. (C22⋊D283)⋊C4 | C2 | semidirect |
| 13. C2×(C2×D283)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D283 | C2 | semidirect |
| 15. #123×C283 | C2 | semidirect |
| 19. C2×Dic566 | C22 | semidirect |
| 22. C2×D1132 | C22 | semidirect |
| 23. C2×D1132 | C22 | semidirect |
| 26. C2×C22⋊D283 | C22 | semidirect |
| 27. C2×C22⋊D283 | C22 | semidirect |
| 29. C22×Dic283 | C22 | semidirect |
| 31. C2×C4×D283 | C22 | semidirect |
| 32. C2×C4×D283 | C22 | semidirect |
| 33. C2×C4×D283 | C22 | semidirect |
| 34. Dic283⋊C4 | C22 | semidirect |
| 35. Dic283⋊C4 | C22 | semidirect |
| 36. C22⋊Dic283 | C22 | semidirect |
| 40. (C2×D283)⋊C4 | C22 | semidirect |
| 41. (C2×D283)⋊C4 | C22 | semidirect |
| 42. (C2×D283)⋊C4 | C22 | semidirect |
| 43. (C2×D283)⋊C4 | C22 | semidirect |
| 44. (C2×D283)⋊C4 | C22 | semidirect |
| 45. C4×Dic283 | C22 | semidirect |
| 47. C22×C4×C283 | C22 | semidirect |
| 48. C4⋊C4×C283 | C22 | semidirect |
| 49. C4⋊C4×C283 | C22 | semidirect |
| 50. C22⋊C4×C283 | C22 | semidirect |
| 51. C22⋊C4×C283 | C22 | semidirect |
| 52. C22⋊C4×C283 | C22 | semidirect |
| 71. C22⋊D283 | D4 | semidirect |
| 110. C2×D283 | #41 | semidirect |
| 129. C283 | #546 | semidirect |
| 135. #123 | D283 | semidirect |
| 165. C22×C4 | C2×D283 | semidirect |
| 168. C4⋊C4 | C2×D283 | semidirect |
| 169. C4⋊C4 | C2×D283 | semidirect |
| 179. C22⋊C4 | C2×D283 | semidirect |
| 180. C22⋊C4 | C2×D283 | semidirect |
| 181. C22⋊C4 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985392 | 2 |
| C2×D4×D283 | 2 |
| #22583596 | 2 |
| #22583595 | 2 |
| #22583588 | 2 |
| #22583585 | 2 |
| #22583583 | 2 |
| #22583582 | 2 |
| #22583580 | 2 |
| #22583572 | 2 |
| (C22⋊D283)⋊C4 | 2 |
| C2×(C2×D283)⋊C4 | 2 |
| C22⋊C4×D283 | 2 |
| #123×C283 | 2 |
| #546 | 283 |