Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
592 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. #81933 | C2 | semidirect |
| 2. #81775 | C2 | semidirect |
| 3. C3×#2240 | C2 | semidirect |
| 4. #71385 | C2 | semidirect |
| 5. #71290 | C2 | semidirect |
| 6. #69197 | C2 | semidirect |
| 7. #69177 | C2 | semidirect |
| 8. #69058 | C2 | semidirect |
| 9. C4×#798 | C2 | semidirect |
| 41. #2240 | D3 | semidirect |
| 149. C3⋊C16 | #41 | semidirect |
| 340. C3 | #33748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81933 | 2 |
| #81775 | 2 |
| C3×#2240 | 2 |
| #71385 | 2 |
| #71290 | 2 |
| #69197 | 2 |
| #69177 | 2 |
| #69058 | 2 |
| C4×#798 | 2 |
| #33748 | 3 |