Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
462 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 97 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×#4516 | C2 | semidirect |
| 3. #71439 | C2 | semidirect |
| 4. C2×#4510 | C2 | semidirect |
| 5. C2×#4509 | C2 | semidirect |
| 6. #69894 | C2 | semidirect |
| 7. C3×#1379 | C2 | semidirect |
| 34. #1379 | D3 | semidirect |
| 73. #819 | D4 | semidirect |
| 371. C3 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78565 | 2 |
| C2×#4516 | 2 |
| #71439 | 2 |
| C2×#4510 | 2 |
| C2×#4509 | 2 |
| #69894 | 2 |
| C3×#1379 | 2 |
| #13411 | 3 |