Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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. #71385 | C2 | semidirect |
| 4. #68588 | C2 | semidirect |
| 5. C3×#1365 | C2 | semidirect |
| 6. #67558 | C2 | semidirect |
| 30. #1365 | D3 | semidirect |
| 102. D24 | Q16 | semidirect |
| 240. C3 | #12407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81953 | 2 |
| #71385 | 2 |
| #69289 | 2 |
| #68588 | 2 |
| C3×#1365 | 2 |
| #67558 | 2 |
| #67471 | 2 |
| #12407 | 3 |