Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
231 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10589323 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 16. C4⋊(C3⋊C16) | D3 | semidirect |
| 185. C32 | #1360 | semidirect |
| 220. C3 | #67562 | semidirect |
| 221. C3 | #67796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4696 | 2 |
| #10589323 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #67796 | 3 |
| #67562 | 3 |