Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
319 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 21. #63550 | C4 | semidirect |
| 238. C32 | #2176 | semidirect |
| 272. C3 | #69209 | semidirect |
| 273. C3 | #70909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4873 | 2 |
| Dic3×Dic12 | 2 |
| C2×#63550 | 2 |
| #10589356 | 2 |
| C3×#4492 | 2 |
| #10589118 | 2 |
| #10589103 | 2 |
| #70909 | 3 |
| #69209 | 3 |