Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 115 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×#2948 | C2 | semidirect |
| 3. #72033 | C2 | semidirect |
| 4. #70656 | C2 | semidirect |
| 5. #69897 | C2 | semidirect |
| 6. #67725 | C2 | semidirect |
| 7. #67672 | C2 | semidirect |
| 17. C2×#827 | C4 | semidirect |
| 20. C2×#826 | C4 | semidirect |
| 29. #2948 | D3 | semidirect |
| 51. C2×Dic12 | C2×C4 | semidirect |
| 56. C2×D24 | C2×C4 | semidirect |
| 73. C2×C3⋊C16 | C2×C4 | semidirect |
| 340. C3 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2948 | 2 |
| C2×#5147 | 2 |
| #72033 | 2 |
| #70656 | 2 |
| #69897 | 2 |
| #67725 | 2 |
| #67672 | 2 |
| #13033 | 3 |