Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
317 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 317 conjugacy classes of subgroups — too many to draw. Only its 76 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×#4880 | C2 | semidirect |
| 3. #10589357 | C2 | semidirect |
| 4. C3×#4490 | C2 | semidirect |
| 5. #10589140 | C2 | semidirect |
| 6. #10589116 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C16) | C2 | semidirect |
| 24. #4880 | D3 | semidirect |
| 33. #4490 | D3 | semidirect |
| 257. C32 | #2234 | semidirect |
| 301. C3 | #69351 | semidirect |
| 302. C3 | #70653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4880 | 2 |
| #10590832 | 2 |
| #10589357 | 2 |
| C3×#4490 | 2 |
| #10589140 | 2 |
| #10589116 | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| #70653 | 3 |
| #69351 | 3 |