Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
646 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 103 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×#3205 | C2 | semidirect |
| 2. #83297 | C2 | semidirect |
| 3. C2×#5072 | C2 | semidirect |
| 4. #71800 | C2 | semidirect |
| 5. #71759 | C2 | semidirect |
| 6. #70783 | C2 | semidirect |
| 7. #67745 | C2 | semidirect |
| 32. #3205 | D3 | semidirect |
| 143. C2×D12 | D8 | semidirect |
| 454. C3 | #10176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3205 | 2 |
| #83297 | 2 |
| C2×#5072 | 2 |
| #71800 | 2 |
| #71759 | 2 |
| #70783 | 2 |
| #67745 | 2 |
| #10176 | 3 |