Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
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×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C29×#123 | C2 |
| hypercenter | #123 | D29 |
| hypocenter | C29 | #546 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×D29 | C2 | semidirect |
| 2. C2×#90805 | C2 | semidirect |
| 3. C29×#123 | C2 | semidirect |
| 4. #11745301 | C2 | semidirect |
| 5. C2×#90781 | C2 | semidirect |
| 6. #11745258 | C2 | semidirect |
| 7. #11745257 | C2 | semidirect |
| 8. #11745256 | C2 | semidirect |
| 9. #11745255 | C2 | semidirect |
| 10. #11745247 | C2 | semidirect |
| 11. #11745246 | C2 | semidirect |
| 12. #11745244 | C2 | semidirect |
| 13. #11745244 | C2 | semidirect |
| 14. #11745243 | C2 | semidirect |
| 15. C22⋊C4×D29 | C2 | semidirect |
| 19. C22×C4×C29 | C22 | semidirect |
| 22. C2×C22⋊D29 | C22 | semidirect |
| 23. C2×C22⋊D29 | C22 | semidirect |
| 24. C22×Dic29 | C22 | semidirect |
| 29. C2×D116 | C22 | semidirect |
| 30. C2×D116 | C22 | semidirect |
| 32. C2×C4×D29 | C22 | semidirect |
| 33. C2×C4×D29 | C22 | semidirect |
| 34. C2×C4×D29 | C22 | semidirect |
| 35. C2×Dic58 | C22 | semidirect |
| 36. C4⋊C4×C29 | C22 | semidirect |
| 37. C4⋊C4×C29 | C22 | semidirect |
| 38. C22⋊C4×C29 | C22 | semidirect |
| 39. C22⋊C4×C29 | C22 | semidirect |
| 40. C22⋊C4×C29 | C22 | semidirect |
| 41. C22⋊Dic29 | C22 | semidirect |
| 45. #90781 | C22 | semidirect |
| 46. #90781 | C22 | semidirect |
| 47. #90781 | C22 | semidirect |
| 48. #90781 | C22 | semidirect |
| 49. #90781 | C22 | semidirect |
| 50. #90779 | C22 | semidirect |
| 51. #90779 | C22 | semidirect |
| 52. C4×Dic29 | C22 | semidirect |
| 75. C22⋊D29 | D4 | semidirect |
| 110. C2×D29 | #41 | semidirect |
| 134. #123 | D29 | semidirect |
| 145. C29 | #546 | semidirect |
| 165. C22×C4 | C2×D29 | semidirect |
| 168. C4⋊C4 | C2×D29 | semidirect |
| 169. C4⋊C4 | C2×D29 | semidirect |
| 179. C22⋊C4 | C2×D29 | semidirect |
| 180. C22⋊C4 | C2×D29 | semidirect |
| 181. C22⋊C4 | C2×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D29 | 2 |
| C2×#90805 | 2 |
| C29×#123 | 2 |
| #11745301 | 2 |
| C2×#90781 | 2 |
| #11745258 | 2 |
| #11745257 | 2 |
| #11745256 | 2 |
| #11745255 | 2 |
| #11745247 | 2 |
| #11745246 | 2 |
| #11745244 | 2 |
| #11745243 | 2 |
| C22⋊C4×D29 | 2 |
| #546 | 29 |