Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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. #79249 | C2 | semidirect |
| 3. C2×C3×#361 | C2 | semidirect |
| 4. #72041 | C2 | semidirect |
| 5. #71442 | C2 | semidirect |
| 6. #67813 | C2 | semidirect |
| 7. #67734 | C2 | semidirect |
| 18. #5147 | C4 | semidirect |
| 32. C2×#361 | D3 | semidirect |
| 336. C3 | #13032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5147 | 2 |
| #79249 | 2 |
| C2×C3×#361 | 2 |
| #72041 | 2 |
| #71442 | 2 |
| #67813 | 2 |
| #67734 | 2 |
| #13032 | 3 |