Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
316 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 82 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×#4895 | C2 | semidirect |
| 2. #10590917 | C2 | semidirect |
| 4. #10589363 | C2 | semidirect |
| 5. C3×#4493 | C2 | semidirect |
| 6. #10589120 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 21. #63551 | C4 | semidirect |
| 22. #63549 | C4 | semidirect |
| 23. #63548 | C4 | semidirect |
| 24. #63546 | C4 | semidirect |
| 29. #4895 | D3 | semidirect |
| 38. #4493 | D3 | semidirect |
| 272. C32 | #2179 | semidirect |
| 309. C3 | #69358 | semidirect |
| 310. C3 | #70922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4895 | 2 |
| #10590917 | 2 |
| #10590632 | 2 |
| #10589363 | 2 |
| C3×#4493 | 2 |
| #10589120 | 2 |
| #10589103 | 2 |
| #70922 | 3 |
| #69358 | 3 |