Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
592 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 147 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. #81933 | C2 | semidirect |
| 2. C3×#2254 | C2 | semidirect |
| 3. #71381 | C2 | semidirect |
| 4. #69348 | C2 | semidirect |
| 5. #69339 | C2 | semidirect |
| 6. #69060 | C2 | semidirect |
| 7. C4×#798 | C2 | semidirect |
| 26. #2254 | D3 | semidirect |
| 97. C3×C16 | #41 | semidirect |
| 170. C16 | #239 | semidirect |
| 220. C3 | #33748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81933 | 2 |
| C3×#2254 | 2 |
| #71381 | 2 |
| #69348 | 2 |
| #69339 | 2 |
| #69060 | 2 |
| C4×#798 | 2 |
| #33748 | 3 |