Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2418 conjugacy classes of subgroups; only the 503 normal subgroups are shown.
This group has 2418 conjugacy classes of subgroups — too many to draw. Only its 503 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×D32×Q8 | C2 | semidirect |
| 2. C2×Q8×#157 | C2 | semidirect |
| 3. Q8×GO+(4,𝔽2) | C2 | direct (N × H) |
| 5. C2×#64222 | C2 | semidirect |
| 6. C2×D32⋊Q8 | C2 | semidirect |
| 11. D32×Q8 | C22 | semidirect |
| 15. Q8×#157 | C22 | semidirect |
| 22. #64222 | C22 | semidirect |
| 23. D32⋊Q8 | C22 | semidirect |
| 28. C2×GO+(4,𝔽2) | Q8 | direct (N × H) |
| 30. C2×C32×Q8 | D4 | semidirect |
| 31. Q8×C3⋊D3 | D4 | semidirect |
| 34. C2×#634 | D4 | semidirect |
| 65. C2×D32 | C2×Q8 | semidirect |
| 68. C2×#157 | C2×Q8 | semidirect |
| 71. GO+(4,𝔽2) | C2×Q8 | direct (N × H) |
| 72. C32×Q8 | C2×D4 | semidirect |
| 77. #634 | C2×D4 | semidirect |
| 122. D32 | C22×Q8 | semidirect |
| 124. #157 | C22×Q8 | semidirect |
| 169. C2×C32 | D4×Q8 | semidirect |
| 171. C3⋊D3 | D4×Q8 | semidirect |
| 185. C2×Q8 | GO+(4,𝔽2) | direct (N × H) |
| 217. C32 | C2×D4×Q8 | semidirect |
| 227. Q8 | C2×GO+(4,𝔽2) | direct (N × H) |
| 269. C2 | Q8×GO+(4,𝔽2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D32×Q8 | 2 |
| C2×Q8×#157 | 2 |
| Q8×GO+(4,𝔽2) | 2 |
| C2×C4×GO+(4,𝔽2) | 2 |
| C2×#64222 | 2 |
| C2×D32⋊Q8 | 2 |
| C2×D4×Q8 | 9 |