Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
550 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 101 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×#3141 | C2 | semidirect |
| 3. #83216 | C2 | semidirect |
| 4. #71811 | C2 | semidirect |
| 5. #71778 | C2 | semidirect |
| 6. #69867 | C2 | semidirect |
| 7. #67668 | C2 | semidirect |
| 34. #3141 | D3 | semidirect |
| 393. C3 | #10200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3141 | 2 |
| #83310 | 2 |
| #83216 | 2 |
| #71811 | 2 |
| #71778 | 2 |
| #69867 | 2 |
| #67668 | 2 |
| #10200 | 3 |