Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 95 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×#1953 | C2 | semidirect |
| 3. #70690 | C2 | semidirect |
| 4. #70687 | C2 | semidirect |
| 5. C2×#4495 | C2 | semidirect |
| 6. C2×#4495 | C2 | semidirect |
| 7. #67672 | C2 | semidirect |
| 33. #1953 | D3 | semidirect |
| 67. C3×#108 | D4 | semidirect |
| 183. #108 | D12 | semidirect |
| 342. C3 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78565 | 2 |
| C3×#1953 | 2 |
| #70690 | 2 |
| #70687 | 2 |
| C2×#4495 | 2 |
| #67672 | 2 |
| #13417 | 3 |