Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
421 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 421 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 70. C3×C3⋊C8 | Q16 | semidirect |
| 144. C3⋊C8 | Dic12 | semidirect |
| 176. C32 | #1707 | semidirect |
| 203. C3 | #68063 | semidirect |
| 204. C3 | #71360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592398 | 2 |
| C3×#4682 | 2 |
| #10590303 | 2 |
| #10590287 | 2 |
| C3×C8×C3⋊C8 | 2 |
| #71360 | 3 |
| #68063 | 3 |