Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
365 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 365 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 2. C3×Dic3×Q16 | C2 | semidirect |
| 4. C3×#4564 | C2 | semidirect |
| 5. #10589140 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 14. #63655 | C4 | semidirect |
| 23. Dic3×Q16 | D3 | semidirect |
| 30. #4564 | D3 | semidirect |
| 41. C32×Q16 | C2×C4 | semidirect |
| 52. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 117. C3×Q16 | C4×D3 | semidirect |
| 118. C3×Q16 | C4×D3 | semidirect |
| 217. Q16 | #624 | semidirect |
| 259. C32 | #2175 | semidirect |
| 299. C3 | #69208 | semidirect |
| 300. C3 | #70913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63655 | 2 |
| C3×Dic3×Q16 | 2 |
| #10590763 | 2 |
| C3×#4564 | 2 |
| #10589140 | 2 |
| #10589116 | 2 |
| #10589103 | 2 |
| #70913 | 3 |
| #69208 | 3 |