Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
216 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 63 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×C4×D16 | C2 | semidirect |
| 2. C2×#4520 | C2 | semidirect |
| 4. #69062 | C2 | semidirect |
| 5. #67578 | C2 | semidirect |
| 6. #67577 | C2 | semidirect |
| 7. C4⋊(C3⋊C32) | C2 | semidirect |
| 25. C4×D16 | D3 | semidirect |
| 189. C3 | #13689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D16 | 2 |
| C2×#4520 | 2 |
| C2×#4519 | 2 |
| #69062 | 2 |
| #67578 | 2 |
| #67577 | 2 |
| C4⋊(C3⋊C32) | 2 |
| #13689 | 3 |