Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
397 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 397 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 |
|---|---|---|
| 70. C3⋊(C3⋊C8) | Q16 | semidirect |
| 173. C32 | #1707 | semidirect |
| 200. C3 | #71296 | semidirect |
| 201. C3 | #71360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4699 | 2 |
| C3×#4682 | 2 |
| #10590309 | 2 |
| #10590290 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #71360 | 3 |
| #71296 | 3 |