Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
885 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 885 conjugacy classes of subgroups — too many to draw. Only its 164 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. C3×#4924 | C2 | semidirect |
| 4. #10589168 | C2 | semidirect |
| 21. #4924 | D3 | semidirect |
| 148. C32×C4 | #100 | semidirect |
| 265. C3×C4 | #823 | semidirect |
| 272. C32 | #1800 | semidirect |
| 320. C4 | #63559 | semidirect |
| 324. C3 | #70527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊(C3⋊D3) | 2 |
| C3×#4924 | 2 |
| C2×#63559 | 2 |
| #10589168 | 2 |
| #70527 | 3 |