Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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. #83899 | C2 | semidirect |
| 3. C3×#2145 | C2 | semidirect |
| 4. C2×#4518 | C2 | semidirect |
| 5. #70658 | C2 | semidirect |
| 6. #67813 | C2 | semidirect |
| 7. #67726 | C2 | semidirect |
| 15. #5195 | C4 | semidirect |
| 17. #5193 | C4 | semidirect |
| 32. #2145 | D3 | semidirect |
| 56. C2×Dic12 | C2×C4 | semidirect |
| 61. C2×D24 | C2×C4 | semidirect |
| 79. #812 | C2×C4 | semidirect |
| 372. C3 | #13030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83899 | 2 |
| #83894 | 2 |
| C3×#2145 | 2 |
| C2×#4518 | 2 |
| #70658 | 2 |
| #67813 | 2 |
| #67726 | 2 |
| #13030 | 3 |