Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
817 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 817 conjugacy classes of subgroups — too many to draw. Only its 156 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. #10591111 | C2 | semidirect |
| 5. #10589157 | C2 | semidirect |
| 13. C3×#940 | C4 | semidirect |
| 15. C3×#936 | C4 | semidirect |
| 24. #5798 | D3 | semidirect |
| 43. C2×C3×D12 | C2×C4 | semidirect |
| 45. C2×C3×Dic6 | C2×C4 | semidirect |
| 55. C3×C4×Dic3 | C2×C4 | semidirect |
| 56. C3×C4×Dic3 | D4 | semidirect |
| 73. #940 | Dic3 | semidirect |
| 75. #936 | Dic3 | semidirect |
| 146. C2×D12 | C2×Dic3 | semidirect |
| 148. C2×Dic6 | C2×Dic3 | semidirect |
| 163. C4×Dic3 | C2×Dic3 | semidirect |
| 164. C4×Dic3 | #67 | semidirect |
| 331. C32 | #1911 | semidirect |
| 388. C3 | #71652 | semidirect |
| 389. C3 | #71853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5805 | 2 |
| C3×#5798 | 2 |
| C2×#63660 | 2 |
| #10591111 | 2 |
| #10589157 | 2 |
| #71853 | 3 |
| #71652 | 3 |