Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
462 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. C3×#1944 | C2 | semidirect |
| 3. #70598 | C2 | semidirect |
| 4. C2×#4488 | C2 | semidirect |
| 5. #67664 | C2 | semidirect |
| 24. #1944 | D3 | semidirect |
| 54. C3×#106 | D4 | semidirect |
| 148. #106 | D12 | semidirect |
| 298. C3 | #13410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78499 | 2 |
| C3×#1944 | 2 |
| #70598 | 2 |
| C2×#4488 | 2 |
| #67664 | 2 |
| #13410 | 3 |