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 |
|---|---|---|
| 2. C2×#5093 | C2 | semidirect |
| 4. C2×#4680 | C2 | semidirect |
| 5. #71256 | C2 | direct (N × H) |
| 6. C2×C8×C3⋊C8 | C2 | semidirect |
| 18. #5093 | C22 | semidirect |
| 24. #4680 | C22 | semidirect |
| 25. C8×C3⋊C8 | C22 | semidirect |
| 231. C2×C3 | #1708 | semidirect |
| 246. C3 | C2×#1708 | semidirect |
| 248. C2 | #71256 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#492 | 2 |
| C2×#5093 | 2 |
| C2×#5070 | 2 |
| C2×#4680 | 2 |
| #71256 | 2 |
| C2×C8×C3⋊C8 | 2 |
| C2×#1708 | 3 |