Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
429 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 1. C3×#4699 | C2 | semidirect |
| 3. #10590312 | C2 | semidirect |
| 5. #10589321 | C2 | semidirect |
| 23. #4699 | D3 | semidirect |
| 178. C32 | #1722 | semidirect |
| 206. C3 | #71263 | semidirect |
| 207. C3 | #71301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4699 | 2 |
| C3×#4693 | 2 |
| #10590312 | 2 |
| #10590277 | 2 |
| #10589321 | 2 |
| #71301 | 3 |
| #71263 | 3 |