Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
322 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 161 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. #31774027 | C2 | semidirect |
| 3. #31774026 | C2 | semidirect |
| 4. C8×Dic542 | C2 | semidirect |
| 81. C271 | #2985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| #31774027 | 2 |
| #31774026 | 2 |
| C8×Dic542 | 2 |
| #31773955 | 2 |
| #31773954 | 2 |
| #431×C271 | 2 |
| #2985 | 271 |