Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
494 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 131 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×#4463 | C2 | semidirect |
| 3. #67791 | C2 | direct (N × H) |
| 13. #4463 | C22 | semidirect |
| 167. C2×C3 | #1357 | semidirect |
| 181. C3 | C2×#1357 | semidirect |
| 185. C2 | #67791 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#493 | 2 |
| C2×#4463 | 2 |
| #67791 | 2 |
| C2×#1357 | 3 |