Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
307 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 307 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. #10589356 | C2 | semidirect |
| 4. C3×#4491 | C2 | semidirect |
| 5. #10589139 | C2 | semidirect |
| 6. #10589114 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C16) | C2 | semidirect |
| 24. #4880 | D3 | semidirect |
| 31. #4491 | D3 | semidirect |
| 251. C32 | #2234 | semidirect |
| 294. C3 | #69201 | semidirect |
| 295. 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 |
| #10590831 | 2 |
| #10589356 | 2 |
| C3×#4491 | 2 |
| #10589139 | 2 |
| #10589114 | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| #70653 | 3 |
| #69201 | 3 |