Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1778 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1778 conjugacy classes of subgroups — too many to draw. Only its 274 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 |
|---|---|---|
| 4. #10593837 | C2 | direct (N × H) |
| 8. C22×C32×Q8 | C4 | semidirect |
| 11. C2×Q8×C3⋊D3 | C4 | semidirect |
| 15. C22×#634 | C4 | semidirect |
| 16. C22×#634 | C4 | semidirect |
| 28. C22×#157 | Q8 | semidirect |
| 32. C2×C32×Q8 | C2×C4 | semidirect |
| 50. C2×#634 | C2×C4 | semidirect |
| 51. C2×#634 | C2×C4 | semidirect |
| 77. C2×#157 | C2×Q8 | semidirect |
| 146. C22×Q8 | #157 | semidirect |
| 180. C2×C32 | #391 | semidirect |
| 183. C3⋊D3 | #391 | semidirect |
| 196. C2×Q8 | C2×#157 | semidirect |
| 234. C32 | C2×#391 | semidirect |
| 296. C2 | #10593837 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×C3⋊D3 | 2 |
| C22×C4⋊#157 | 2 |
| C22×C4×#157 | 2 |
| #10593837 | 2 |
| C2×#63781 | 2 |
| C2×#391 | 9 |