Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
261 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 70 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. C32×C22⋊C16 | C2 | semidirect |
| 3. C3×#4552 | C2 | semidirect |
| 5. #67527 | C3 | direct (N × H) |
| 16. C3×C22⋊C16 | D3 | semidirect |
| 17. C3×C22⋊C16 | C2×C3 | semidirect |
| 19. #4552 | C2×C3 | semidirect |
| 64. C22⋊C16 | C3×D3 | semidirect |
| 195. C32 | #1349 | semidirect |
| 235. C3 | #67527 | direct (N × H) |
| 236. C3 | C3×#1349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5115 | 2 |
| C32×C22⋊C16 | 2 |
| C3×#4552 | 2 |
| C3×#1349 | 3 |
| #67527 | 3 |