Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
457 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 457 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 3. #10589321 | C2 | semidirect |
| 4. C3×#4455 | C2 | semidirect |
| 5. C3⋊C82 | C2 | semidirect |
| 25. #4455 | D3 | semidirect |
| 37. C3×D3×C8 | C8 | semidirect |
| 97. D3×C8 | C3⋊C8 | semidirect |
| 170. C32 | #1450 | semidirect |
| 198. C3 | #68068 | semidirect |
| 199. C3 | #69724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D3×C8 | 2 |
| #10590261 | 2 |
| #10589321 | 2 |
| C3×#4455 | 2 |
| C3⋊C82 | 2 |
| #69724 | 3 |
| #68068 | 3 |