Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×C3×#361 | C2 | semidirect |
| 3. C2×#4562 | C2 | semidirect |
| 4. #71439 | C2 | semidirect |
| 5. #70701 | C2 | semidirect |
| 6. C2×#4497 | C2 | semidirect |
| 7. #67815 | C2 | semidirect |
| 29. C2×#361 | D3 | semidirect |
| 68. C3×#108 | D4 | semidirect |
| 186. #108 | #67 | semidirect |
| 371. C3 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83830 | 2 |
| C2×C3×#361 | 2 |
| C2×#4562 | 2 |
| #71439 | 2 |
| #70701 | 2 |
| C2×#4497 | 2 |
| #67815 | 2 |
| #13411 | 3 |