Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
383 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 36. #3746 | C8 | semidirect |
| 79. C3×C3⋊C8 | Q16 | semidirect |
| 169. C3⋊C8 | Dic12 | semidirect |
| 209. C32 | C8×Q16 | semidirect |
| 241. C3 | C8×Dic12 | semidirect |
| 242. C3 | #68557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3746 | 2 |
| #10590254 | 2 |
| C3×#4458 | 2 |
| C3×C8×C3⋊C8 | 2 |
| #10589085 | 2 |
| #68557 | 3 |
| C8×Dic12 | 3 |