Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
369 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 1. #10592381 | C2 | semidirect |
| 3. C3×C4×C3⋊C16 | C2 | semidirect |
| 4. #10589115 | C2 | semidirect |
| 23. C4×C3⋊C16 | D3 | semidirect |
| 191. C32 | #2240 | semidirect |
| 225. C3 | #69058 | semidirect |
| 226. C3 | #71288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592381 | 2 |
| C3×#4695 | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589115 | 2 |
| #71288 | 3 |
| #69058 | 3 |