Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
534 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 93 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. #83928 | C2 | semidirect |
| 2. C2×#5193 | C2 | semidirect |
| 3. C2×#4897 | C2 | semidirect |
| 4. C3×#2143 | C2 | semidirect |
| 5. C2×#4516 | C2 | semidirect |
| 6. #71435 | C2 | semidirect |
| 7. #67734 | C2 | semidirect |
| 36. #2143 | D3 | semidirect |
| 411. C3 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83928 | 2 |
| C2×#5193 | 2 |
| C2×#4897 | 2 |
| C3×#2143 | 2 |
| C2×#4516 | 2 |
| #71435 | 2 |
| #67734 | 2 |
| #13323 | 3 |