Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
510 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 143 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. #71967 | C2 | semidirect |
| 4. #67688 | C2 | semidirect |
| 5. #67683 | C2 | semidirect |
| 7. C2×C3×#131 | C4 | semidirect |
| 12. C3×#424 | C4 | semidirect |
| 13. C3×#408 | C4 | semidirect |
| 15. C3×#405 | C4 | semidirect |
| 20. #4538 | C4 | semidirect |
| 21. #4537 | C4 | semidirect |
| 57. C2×#131 | Dic3 | semidirect |
| 62. #424 | Dic3 | semidirect |
| 63. #408 | Dic3 | semidirect |
| 66. #405 | Dic3 | semidirect |
| 281. C3 | #8239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2929 | 2 |
| #71967 | 2 |
| #71707 | 2 |
| #67688 | 2 |
| #67683 | 2 |
| #8239 | 3 |