Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
229 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 229 conjugacy classes of subgroups — too many to draw. Only its 78 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×C4⋊C16 | C2 | semidirect |
| 3. C3×#4457 | C2 | semidirect |
| 5. #67562 | C3 | direct (N × H) |
| 16. C3×C4⋊C16 | D3 | semidirect |
| 17. C3×C4⋊C16 | C2×C3 | semidirect |
| 19. #4457 | C2×C3 | semidirect |
| 64. C4⋊C16 | C3×D3 | semidirect |
| 184. C32 | #1360 | semidirect |
| 219. C3 | #67562 | direct (N × H) |
| 220. C3 | C3×#1360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4696 | 2 |
| C32×C4⋊C16 | 2 |
| C3×#4457 | 2 |
| C3×#1360 | 3 |
| #67562 | 3 |