Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31774621 | C2 | semidirect |
| 2. #31774562 | C2 | semidirect |
| 3. #31774258 | C2 | semidirect |
| 4. #31774190 | C2 | semidirect |
| 5. #31774174 | C2 | semidirect |
| 7. #31774099 | C2 | semidirect |
| 8. #31774027 | C2 | semidirect |
| 9. #31774000 | C2 | semidirect |
| 11. #487×C271 | C2 | semidirect |
| 122. C271 | #3367 | semidirect |
| 127. #487 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774621 | 2 |
| #31774562 | 2 |
| #31774258 | 2 |
| #31774190 | 2 |
| #31774174 | 2 |
| #31774115 | 2 |
| #31774099 | 2 |
| #31774027 | 2 |
| #31774000 | 2 |
| C4×D2168 | 2 |
| #487×C271 | 2 |
| #3367 | 271 |