Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
398 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 103 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. C3×#1712 | C2 | semidirect |
| 2. #71290 | C2 | semidirect |
| 3. #68062 | C2 | semidirect |
| 4. C8×C3⋊C16 | C2 | semidirect |
| 15. #1712 | D3 | semidirect |
| 45. C3⋊C16 | D8 | semidirect |
| 64. C3×C8 | D16 | semidirect |
| 93. C8 | #826 | semidirect |
| 106. C3 | #12515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1712 | 2 |
| #71290 | 2 |
| #68062 | 2 |
| C8×C3⋊C16 | 2 |
| #12515 | 3 |