Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
387 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 98 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×C4×Dic12 | C2 | semidirect |
| 4. C3×#4461 | C2 | semidirect |
| 5. #10589139 | C2 | semidirect |
| 6. #10589118 | C2 | semidirect |
| 21. #63549 | C4 | semidirect |
| 25. C4×Dic12 | D3 | semidirect |
| 36. #4461 | D3 | semidirect |
| 51. C3×Dic12 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 138. Dic12 | C4×D3 | semidirect |
| 148. C3⋊C16 | C4×D3 | semidirect |
| 265. C32 | #2175 | semidirect |
| 305. C3 | #69077 | semidirect |
| 306. C3 | #70913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3745 | 2 |
| C3×C4×Dic12 | 2 |
| C2×#63549 | 2 |
| C3×#4461 | 2 |
| #10589139 | 2 |
| #10589118 | 2 |
| #10589116 | 2 |
| #70913 | 3 |
| #69077 | 3 |