Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
578 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#5078 | C2 | semidirect |
| 4. C3×#1546 | C2 | semidirect |
| 5. #70522 | C2 | semidirect |
| 7. #67739 | C2 | semidirect |
| 34. #1546 | D3 | semidirect |
| 345. C3 | #10174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5078 | 2 |
| #83203 | 2 |
| #79268 | 2 |
| C3×#1546 | 2 |
| #70522 | 2 |
| #70498 | 2 |
| #67739 | 2 |
| #10174 | 3 |