Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
338 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 17. C3×#333 | C4 | semidirect |
| 18. C3×#332 | C4 | semidirect |
| 72. #333 | Dic3 | semidirect |
| 73. #332 | Dic3 | semidirect |
| 271. C3 | #9579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1542 | 2 |
| #71839 | 2 |
| #71824 | 2 |
| #70749 | 2 |
| Dic3×C4⋊C8 | 2 |
| #67736 | 2 |
| #67707 | 2 |
| #9579 | 3 |