Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
946 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 946 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×#157 | C2 | semidirect |
| 3. C2×#63782 | C2 | semidirect |
| 4. #10593778 | C2 | direct (N × H) |
| 5. C2×#63768 | C2 | semidirect |
| 6. C2×#63767 | C2 | semidirect |
| 11. D4×#157 | C22 | semidirect |
| 15. C2×C32×D8 | C4 | semidirect |
| 16. C2×#3753 | C4 | semidirect |
| 17. D8×C3⋊D3 | C4 | semidirect |
| 19. C2×#3745 | C4 | semidirect |
| 21. #63782 | C22 | semidirect |
| 22. #63768 | C22 | semidirect |
| 23. #63767 | C22 | semidirect |
| 30. C2×C32×D4 | C2×C4 | semidirect |
| 34. D4×C3⋊D3 | C2×C4 | semidirect |
| 36. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 46. C32×D8 | C2×C4 | semidirect |
| 47. C2×C32×C8 | C2×C4 | semidirect |
| 48. #3753 | C2×C4 | semidirect |
| 49. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 50. #3745 | C2×C4 | semidirect |
| 51. C8×C3⋊D3 | C2×C4 | semidirect |
| 74. C32×D4 | C22×C4 | semidirect |
| 80. C4⋊(C3⋊D3) | C22×C4 | semidirect |
| 86. C32×C8 | C22×C4 | semidirect |
| 87. C3⋊(C3⋊C8) | C22×C4 | semidirect |
| 133. C2×D8 | #157 | semidirect |
| 166. C2×C32 | #442 | semidirect |
| 169. C3⋊D3 | #442 | semidirect |
| 178. C2×D4 | C2×#157 | semidirect |
| 186. D8 | C2×#157 | semidirect |
| 193. C2×C8 | C2×#157 | semidirect |
| 214. C32 | C2×#442 | semidirect |
| 227. D4 | C22×#157 | semidirect |
| 241. C8 | C22×#157 | semidirect |
| 270. C2 | #10593778 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#157 | 2 |
| C2×D8×C3⋊D3 | 2 |
| C2×#63782 | 2 |
| #10593778 | 2 |
| C2×#63768 | 2 |
| C2×#63767 | 2 |
| C2×#442 | 9 |