Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #31774633 | C2 | semidirect |
| 2. #31774608 | C2 | semidirect |
| 3. #31774250 | C2 | semidirect |
| 4. #31774199 | C2 | semidirect |
| 5. #31774189 | C2 | semidirect |
| 6. #31774111 | C2 | semidirect |
| 8. C8×Dic542 | C2 | semidirect |
| 9. C4×#16864643 | C2 | semidirect |
| 10. #31773977 | C2 | semidirect |
| 11. #486×C271 | C2 | semidirect |
| 122. C271 | #3361 | semidirect |
| 127. #486 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774633 | 2 |
| #31774608 | 2 |
| #31774250 | 2 |
| #31774199 | 2 |
| #31774189 | 2 |
| #31774111 | 2 |
| #31774089 | 2 |
| C8×Dic542 | 2 |
| C4×#16864643 | 2 |
| #31773977 | 2 |
| #486×C271 | 2 |
| #3361 | 271 |