Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 251 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. C2×C3×#498 | C2 | semidirect |
| 2. C2×#5079 | C2 | semidirect |
| 5. #71334 | C2 | direct (N × H) |
| 6. C2×C8×C3⋊C8 | C2 | semidirect |
| 13. C3×#498 | C22 | semidirect |
| 20. #5079 | C22 | semidirect |
| 25. C8×C3⋊C8 | C22 | semidirect |
| 26. C2×#498 | D3 | semidirect |
| 66. #498 | C2×D3 | semidirect |
| 230. C2×C3 | #1708 | semidirect |
| 246. C3 | C2×#1708 | semidirect |
| 248. C2 | #71334 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#498 | 2 |
| C2×#5079 | 2 |
| C2×#5088 | 2 |
| C2×#4693 | 2 |
| #71334 | 2 |
| C2×C8×C3⋊C8 | 2 |
| C2×#1708 | 3 |