Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
518 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 91 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. C3×#1836 | C2 | semidirect |
| 3. C2×#4464 | C2 | semidirect |
| 4. #69581 | C2 | semidirect |
| 5. #67630 | C2 | semidirect |
| 21. #1836 | D3 | semidirect |
| 42. C3×#97 | D4 | semidirect |
| 119. #97 | D12 | semidirect |
| 264. C3 | #10425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #74254 | 2 |
| C3×#1836 | 2 |
| C2×#4464 | 2 |
| #69581 | 2 |
| #67630 | 2 |
| #10425 | 3 |