Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#3150 | C2 | semidirect |
| 2. #83894 | C2 | semidirect |
| 3. #72080 | C2 | semidirect |
| 4. #69845 | C2 | semidirect |
| 5. #67663 | C2 | semidirect |
| 25. #3150 | D3 | semidirect |
| 52. C2×Dic12 | D4 | semidirect |
| 55. C2×D24 | D4 | semidirect |
| 66. C2×C3⋊C16 | D4 | semidirect |
| 320. C3 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3150 | 2 |
| #83894 | 2 |
| #72080 | 2 |
| #69845 | 2 |
| #67663 | 2 |
| #13340 | 3 |