Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
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×D47 |
| commutator, socle, cosocle | C22×C47 | C24 |
| Fitting | #123×C47 | C2 |
| hypercenter | #123 | D47 |
| hypocenter | C47 | #546 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625350 | C2 | semidirect |
| 2. C2×D4×D47 | C2 | semidirect |
| 3. #13094010 | C2 | semidirect |
| 4. #13094009 | C2 | semidirect |
| 5. #13094002 | C2 | semidirect |
| 6. #13093999 | C2 | semidirect |
| 7. #13093997 | C2 | semidirect |
| 8. #13093996 | C2 | semidirect |
| 9. #13093994 | C2 | semidirect |
| 10. #13093994 | C2 | semidirect |
| 11. #13093986 | C2 | semidirect |
| 12. (C22⋊D47)⋊C4 | C2 | semidirect |
| 13. C2×(C2×D47)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D47 | C2 | semidirect |
| 15. #123×C47 | C2 | semidirect |
| 19. C22×C4×C47 | C22 | semidirect |
| 22. C2×C22⋊D47 | C22 | semidirect |
| 23. C2×C22⋊D47 | C22 | semidirect |
| 24. C22×Dic47 | C22 | semidirect |
| 29. C2×D188 | C22 | semidirect |
| 30. C2×D188 | C22 | semidirect |
| 32. C2×C4×D47 | C22 | semidirect |
| 33. C2×C4×D47 | C22 | semidirect |
| 34. C2×C4×D47 | C22 | semidirect |
| 35. C2×Dic94 | C22 | semidirect |
| 36. C4⋊C4×C47 | C22 | semidirect |
| 37. C4⋊C4×C47 | C22 | semidirect |
| 38. C22⋊C4×C47 | C22 | semidirect |
| 39. C22⋊C4×C47 | C22 | semidirect |
| 40. C22⋊C4×C47 | C22 | semidirect |
| 41. C22⋊Dic47 | C22 | semidirect |
| 45. (C2×D47)⋊C4 | C22 | semidirect |
| 46. (C2×D47)⋊C4 | C22 | semidirect |
| 47. (C2×D47)⋊C4 | C22 | semidirect |
| 48. (C2×D47)⋊C4 | C22 | semidirect |
| 49. (C2×D47)⋊C4 | C22 | semidirect |
| 50. Dic47⋊C4 | C22 | semidirect |
| 51. Dic47⋊C4 | C22 | semidirect |
| 52. C4×Dic47 | C22 | semidirect |
| 75. C22⋊D47 | D4 | semidirect |
| 110. C2×D47 | #41 | semidirect |
| 130. C47 | #546 | semidirect |
| 135. #123 | D47 | semidirect |
| 165. C22×C4 | C2×D47 | semidirect |
| 168. C4⋊C4 | C2×D47 | semidirect |
| 169. C4⋊C4 | C2×D47 | semidirect |
| 179. C22⋊C4 | C2×D47 | semidirect |
| 180. C22⋊C4 | C2×D47 | semidirect |
| 181. C22⋊C4 | C2×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625350 | 2 |
| C2×D4×D47 | 2 |
| #13094010 | 2 |
| #13094009 | 2 |
| #13094002 | 2 |
| #13093999 | 2 |
| #13093997 | 2 |
| #13093996 | 2 |
| #13093994 | 2 |
| #13093986 | 2 |
| (C22⋊D47)⋊C4 | 2 |
| C2×(C2×D47)⋊C4 | 2 |
| C22⋊C4×D47 | 2 |
| #123×C47 | 2 |
| #546 | 47 |