Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2724 conjugacy classes of subgroups; only the 689 normal subgroups are shown.
This group has 2724 conjugacy classes of subgroups — too many to draw. Only its 689 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×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C2×C32×#95 | C2 | semidirect |
| 4. #10592376 | C2 | direct (N × H) |
| 12. C2×C4⋊(C3⋊Dic3) | C22 | semidirect |
| 13. C32×#95 | C22 | semidirect |
| 16. C2×C3×#95 | D3 | semidirect |
| 39. C3×#95 | C2×D3 | semidirect |
| 59. C2×#95 | C3⋊D3 | semidirect |
| 92. #95 | C2×C3⋊D3 | semidirect |
| 109. C2×C32 | #399 | semidirect |
| 139. C32 | C2×#399 | semidirect |
| 156. C2×C3 | #4677 | semidirect |
| 173. C3 | C2×#4677 | semidirect |
| 175. C2 | #10592376 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3752 | 2 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| C2×C32×#95 | 2 |
| #10592376 | 2 |
| C2×#4677 | 3 |