Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
550 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 550 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 |
|---|---|---|
| 1. C3×#3227 | C2 | semidirect |
| 3. C2×#5087 | C2 | semidirect |
| 4. #71800 | C2 | semidirect |
| 5. #71774 | C2 | semidirect |
| 6. #70783 | C2 | semidirect |
| 7. #67745 | C2 | semidirect |
| 32. #3227 | D3 | semidirect |
| 409. C3 | #10188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3227 | 2 |
| #83297 | 2 |
| C2×#5087 | 2 |
| #71800 | 2 |
| #71774 | 2 |
| #70783 | 2 |
| #67745 | 2 |
| #10188 | 3 |