Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
331 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 331 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 78. C32×C8 | Q16 | semidirect |
| 161. C3×C8 | #216 | semidirect |
| 162. C3×C8 | #216 | semidirect |
| 204. C32 | #1694 | semidirect |
| 217. C8 | #3718 | semidirect |
| 236. C3 | #70964 | semidirect |
| 237. C3 | #71379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4682 | 2 |
| C3×#4679 | 2 |
| #10590384 | 2 |
| #10589323 | 2 |
| #10589092 | 2 |
| #71379 | 3 |
| #70964 | 3 |