Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774509 | C2 | semidirect |
| 2. #31774296 | C2 | semidirect |
| 3. #31774269 | C2 | semidirect |
| 4. #31774267 | C2 | semidirect |
| 5. #31774261 | C2 | semidirect |
| 6. #31774141 | C2 | semidirect |
| 7. #31774124 | C2 | semidirect |
| 8. #31773997 | C2 | semidirect |
| 9. C4×#16864642 | C2 | semidirect |
| 10. #31773853 | C2 | semidirect |
| 108. C271 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774509 | 2 |
| #31774296 | 2 |
| #31774269 | 2 |
| #31774267 | 2 |
| #31774261 | 2 |
| #31774141 | 2 |
| #31774124 | 2 |
| #31773997 | 2 |
| C4×#16864642 | 2 |
| #31773853 | 2 |
| #540×C271 | 2 |
| #3174 | 271 |