Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
534 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 97 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. C3×#3067 | C2 | semidirect |
| 2. C2×#5193 | C2 | semidirect |
| 3. C2×#5142 | C2 | semidirect |
| 4. #72080 | C2 | semidirect |
| 5. #72007 | C2 | semidirect |
| 6. C2×#4495 | C2 | semidirect |
| 7. #67733 | C2 | semidirect |
| 33. #3067 | 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 |
|---|---|
| C3×#3067 | 2 |
| C2×#5193 | 2 |
| C2×#5142 | 2 |
| #72080 | 2 |
| #72007 | 2 |
| C2×#4495 | 2 |
| #67733 | 2 |
| #13323 | 3 |