Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
929 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 929 conjugacy classes of subgroups — too many to draw. Only its 236 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. C22×#3746 | C2 | semidirect |
| 3. C22×C3×C3⋊C16 | C2 | semidirect |
| 4. C2×#63548 | C2 | direct (N × H) |
| 11. C2×#3746 | C22 | semidirect |
| 14. C2×C3×C3⋊C16 | C22 | semidirect |
| 15. #63548 | C22 | direct (N × H) |
| 23. C22×C3⋊C16 | D3 | semidirect |
| 35. #3746 | C23 | semidirect |
| 38. C3×C3⋊C16 | C23 | semidirect |
| 60. C2×C3⋊C16 | C2×D3 | semidirect |
| 113. C3⋊C16 | C22×D3 | semidirect |
| 114. C22×C32 | SD32 | semidirect |
| 162. C2×C32 | C2×SD32 | semidirect |
| 183. C22×C3 | #800 | semidirect |
| 184. C22×C3 | #827 | semidirect |
| 198. C32 | C22×SD32 | semidirect |
| 214. C2×C3 | C2×#800 | semidirect |
| 215. C2×C3 | C2×#827 | semidirect |
| 221. C22 | #63548 | direct (N × H) |
| 227. C3 | C22×#800 | semidirect |
| 228. C3 | C22×#827 | semidirect |
| 230. C2 | C2×#63548 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3746 | 2 |
| C22×C3×D24 | 2 |
| C22×C3×C3⋊C16 | 2 |
| C2×#63548 | 2 |
| C22×#827 | 3 |
| C22×#800 | 3 |