Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
406 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5076 | C2 | semidirect |
| 3. #10590337 | C2 | semidirect |
| 4. #10590269 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589099 | C2 | semidirect |
| 7. #10589092 | C2 | semidirect |
| 28. #5076 | D3 | semidirect |
| 116. C3×C3⋊C8 | D8 | semidirect |
| 255. C3⋊C8 | #213 | semidirect |
| 318. C32 | #1685 | semidirect |
| 371. C3 | #71008 | semidirect |
| 372. C3 | #71268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5076 | 2 |
| C3×#5072 | 2 |
| #10590337 | 2 |
| #10590269 | 2 |
| #10589410 | 2 |
| #10589099 | 2 |
| #10589092 | 2 |
| #71268 | 3 |
| #71008 | 3 |