Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 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. #79335 | C2 | semidirect |
| 3. C3×#1555 | C2 | semidirect |
| 4. #71760 | C2 | semidirect |
| 5. #70827 | C2 | semidirect |
| 6. #67750 | C2 | semidirect |
| 7. #67749 | C2 | semidirect |
| 33. #1555 | D3 | semidirect |
| 67. C3×C4⋊C8 | D4 | semidirect |
| 78. C4⋊(C3⋊C8) | D4 | semidirect |
| 190. C4⋊C8 | #67 | semidirect |
| 434. C3 | #9457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83188 | 2 |
| #79335 | 2 |
| C3×#1555 | 2 |
| #71760 | 2 |
| #70827 | 2 |
| #67750 | 2 |
| #67749 | 2 |
| #9457 | 3 |