Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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. #79286 | C2 | semidirect |
| 3. C3×#1486 | C2 | semidirect |
| 4. #71598 | C2 | semidirect |
| 5. #70527 | C2 | semidirect |
| 6. #67738 | C2 | semidirect |
| 7. #67713 | C2 | semidirect |
| 32. #1486 | D3 | semidirect |
| 65. C3×C4×C8 | D4 | semidirect |
| 75. C4×C3⋊C8 | D4 | semidirect |
| 186. C4×C8 | #67 | semidirect |
| 411. C3 | #9485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82415 | 2 |
| #79286 | 2 |
| C3×#1486 | 2 |
| #71598 | 2 |
| #70527 | 2 |
| #67738 | 2 |
| #67713 | 2 |
| #9485 | 3 |