Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
310 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 21. Dic3⋊C16 | C4 | semidirect |
| 188. Dic3 | #365 | semidirect |
| 226. C3 | #13183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4513 | 2 |
| #71420 | 2 |
| Dic3×#108 | 2 |
| #70554 | 2 |
| C2×#4487 | 2 |
| C3×#1383 | 2 |
| #67730 | 2 |
| #13183 | 3 |