Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
981 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 981 conjugacy classes of subgroups — too many to draw. Only its 164 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×#5798 | C2 | semidirect |
| 3. C2×#63660 | C2 | semidirect |
| 4. #10591085 | C2 | semidirect |
| 5. #10589161 | C2 | semidirect |
| 14. C3×#940 | C4 | semidirect |
| 23. #5798 | D3 | semidirect |
| 45. C2×C3×D12 | C2×C4 | semidirect |
| 51. C3×C4⋊Dic3 | D4 | semidirect |
| 54. C3×C4×Dic3 | C2×C4 | semidirect |
| 71. #940 | Dic3 | semidirect |
| 146. C2×D12 | C2×Dic3 | semidirect |
| 155. C4⋊Dic3 | #67 | semidirect |
| 158. C4×Dic3 | C2×Dic3 | semidirect |
| 326. C32 | #1887 | semidirect |
| 384. C3 | #71650 | semidirect |
| 385. C3 | #71763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#940 | 2 |
| C3×#5798 | 2 |
| C2×#63660 | 2 |
| #10591085 | 2 |
| #10589161 | 2 |
| #71763 | 3 |
| #71650 | 3 |