Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
466 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 131 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. #83780 | C2 | semidirect |
| 3. C3×#2115 | C2 | semidirect |
| 4. #71438 | C2 | semidirect |
| 5. #67811 | C2 | semidirect |
| 25. #2115 | D3 | semidirect |
| 60. C2×C3⋊C16 | D4 | semidirect |
| 279. C3 | #12988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83787 | 2 |
| #83780 | 2 |
| C3×#2115 | 2 |
| #71438 | 2 |
| #67811 | 2 |
| #12988 | 3 |