Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
282 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 22. #4490 | C4 | semidirect |
| 23. #4489 | C4 | semidirect |
| 101. C3⋊C16 | C4⋊C4 | semidirect |
| 239. C3 | #13174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4512 | 2 |
| #70705 | 2 |
| C2×#4494 | 2 |
| #70613 | 2 |
| #70596 | 2 |
| C3×#1387 | 2 |
| #67819 | 2 |
| #13174 | 3 |