Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 474 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. #82518 | C2 | semidirect |
| 3. C3×#1488 | C2 | semidirect |
| 4. #70804 | C2 | semidirect |
| 5. #70784 | C2 | semidirect |
| 6. #67758 | C2 | semidirect |
| 7. #67743 | C2 | semidirect |
| 37. #1488 | D3 | semidirect |
| 408. C3 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82527 | 2 |
| #82518 | 2 |
| C3×#1488 | 2 |
| #70804 | 2 |
| #70784 | 2 |
| #67758 | 2 |
| #67743 | 2 |
| #9349 | 3 |