Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1386 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 243 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. #78619 | C2 | semidirect |
| 3. C3×#1784 | C2 | semidirect |
| 4. #72133 | C2 | semidirect |
| 5. #70099 | C2 | semidirect |
| 16. C2×C3×#101 | C22 | semidirect |
| 18. C2×#836 | C22 | semidirect |
| 21. #5118 | C22 | semidirect |
| 22. Dic3×M16 | C22 | semidirect |
| 29. #1784 | D3 | semidirect |
| 79. C2×#101 | C2×D3 | semidirect |
| 301. C3 | #21798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#947 | 2 |
| #78619 | 2 |
| C3×#1784 | 2 |
| #72133 | 2 |
| #70099 | 2 |
| #69988 | 2 |
| #21798 | 3 |