Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
476 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 476 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×#2957 | C2 | semidirect |
| 3. #72081 | C2 | semidirect |
| 4. C2×#4495 | C2 | semidirect |
| 5. #69903 | C2 | semidirect |
| 6. #67734 | C2 | semidirect |
| 7. #67672 | C2 | semidirect |
| 18. #5193 | C4 | semidirect |
| 30. #2957 | D3 | semidirect |
| 336. C3 | #13032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2957 | 2 |
| C2×#5193 | 2 |
| #72081 | 2 |
| C2×#4495 | 2 |
| #69903 | 2 |
| #67734 | 2 |
| #67672 | 2 |
| #13032 | 3 |