Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
373 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 373 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 7. #71308 | C3 | direct (N × H) |
| 80. C3×Dic6 | Q16 | semidirect |
| 171. Dic6 | C3×Q16 | semidirect |
| 224. C32 | #1670 | semidirect |
| 258. C3 | #71308 | direct (N × H) |
| 259. C3 | C3×#1670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#494 | 2 |
| C3×#5094 | 2 |
| C3×C8×Dic6 | 2 |
| C3×#4547 | 2 |
| C3×#4458 | 2 |
| C3×#1670 | 3 |
| #71308 | 3 |