Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
794 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 139 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×#5015 | C2 | semidirect |
| 2. C2×#4695 | C2 | semidirect |
| 3. C3×#1954 | C2 | semidirect |
| 4. C2×#4485 | C2 | semidirect |
| 5. #67654 | C2 | semidirect |
| 22. #1954 | D3 | semidirect |
| 72. C2×C3×D4 | D8 | semidirect |
| 98. C2×C3×C8 | D8 | semidirect |
| 195. C2×D4 | D24 | semidirect |
| 213. C2×C8 | #213 | semidirect |
| 309. C3 | #10260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5015 | 2 |
| C2×#4695 | 2 |
| C3×#1954 | 2 |
| C2×#4485 | 2 |
| #67654 | 2 |
| #10260 | 3 |