Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
969 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 969 conjugacy classes of subgroups — too many to draw. Only its 316 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 |
|---|---|---|
| 2. C22×C3×C3⋊C16 | C2 | semidirect |
| 3. C2×#63544 | C2 | direct (N × H) |
| 10. C2×C3×C3⋊C16 | C22 | semidirect |
| 11. #63544 | C22 | direct (N × H) |
| 15. C22×C3⋊C16 | D3 | semidirect |
| 27. C3×C3⋊C16 | C23 | semidirect |
| 40. C2×C3⋊C16 | C2×D3 | semidirect |
| 77. C3⋊C16 | C22×D3 | semidirect |
| 78. C22×C32 | M32 | semidirect |
| 114. C2×C32 | C2×M32 | semidirect |
| 130. C22×C3 | #798 | semidirect |
| 142. C32 | C22×M32 | semidirect |
| 156. C2×C3 | C2×#798 | semidirect |
| 162. C22 | #63544 | direct (N × H) |
| 168. C3 | C22×#798 | semidirect |
| 170. C2 | C2×#63544 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C3⋊D3 | 2 |
| C22×C3×C3⋊C16 | 2 |
| C2×#63544 | 2 |
| C22×#798 | 3 |