Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
382 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 2. C3×#5070 | C2 | semidirect |
| 3. #10590337 | C2 | semidirect |
| 4. #10590266 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589099 | C2 | semidirect |
| 7. #10589095 | C2 | semidirect |
| 29. #5070 | D3 | semidirect |
| 307. C32 | #1697 | semidirect |
| 359. C3 | #71010 | semidirect |
| 360. C3 | #71202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5072 | 2 |
| C3×#5070 | 2 |
| #10590337 | 2 |
| #10590266 | 2 |
| #10589410 | 2 |
| #10589099 | 2 |
| #10589095 | 2 |
| #71202 | 3 |
| #71010 | 3 |