Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
349 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 100 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×Dic3×Q16 | C2 | semidirect |
| 4. #10589430 | C2 | semidirect |
| 5. #10589139 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 17. C3×#828 | C4 | semidirect |
| 24. Dic3×Q16 | D3 | semidirect |
| 41. C32×Q16 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 71. #828 | Dic3 | semidirect |
| 115. C3×Q16 | C4×D3 | semidirect |
| 116. C3×Q16 | C2×Dic3 | semidirect |
| 143. C3⋊C16 | C2×Dic3 | semidirect |
| 212. Q16 | D3×Dic3 | semidirect |
| 252. C32 | #2175 | semidirect |
| 291. C3 | #70913 | semidirect |
| 292. C3 | #71474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Dic3×Q16 | 2 |
| C2×C3×#828 | 2 |
| Dic3×D24 | 2 |
| #10589430 | 2 |
| #10589139 | 2 |
| #10589114 | 2 |
| #10589103 | 2 |
| #71474 | 3 |
| #70913 | 3 |