Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
277 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 277 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 50. C3×C3⋊C16 | Q8 | semidirect |
| 131. C3⋊C16 | Dic6 | semidirect |
| 225. C32 | #2183 | semidirect |
| 258. C3 | #69068 | semidirect |
| 259. C3 | #69282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#627 | 2 |
| #10589367 | 2 |
| C3×#4502 | 2 |
| C3×Dic3⋊C16 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #10589103 | 2 |
| #10589102 | 2 |
| #69282 | 3 |
| #69068 | 3 |