Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
232 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 71 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×#2247 | C2 | semidirect |
| 2. C2×#4522 | C2 | semidirect |
| 5. #67508 | C2 | semidirect |
| 21. #2247 | D3 | semidirect |
| 151. C3 | #13730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2247 | 2 |
| C2×#4522 | 2 |
| C2×#4521 | 2 |
| #69062 | 2 |
| #67508 | 2 |
| #13730 | 3 |