Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774612 | C2 | semidirect |
| 2. #31774551 | C2 | semidirect |
| 3. #31774295 | C2 | semidirect |
| 4. #31774222 | C2 | semidirect |
| 5. #31774216 | C2 | semidirect |
| 6. #31774188 | C2 | semidirect |
| 7. #31774178 | C2 | semidirect |
| 8. #31774150 | C2 | semidirect |
| 9. C4×D2168 | C2 | semidirect |
| 10. #31773939 | C2 | semidirect |
| 11. #436×C271 | C2 | semidirect |
| 101. C8×C271 | #41 | semidirect |
| 127. C271 | #3354 | semidirect |
| 138. #436 | D271 | semidirect |
| 229. C8 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774612 | 2 |
| #31774551 | 2 |
| #31774295 | 2 |
| #31774222 | 2 |
| #31774216 | 2 |
| #31774188 | 2 |
| #31774178 | 2 |
| #31774150 | 2 |
| C4×D2168 | 2 |
| #31773939 | 2 |
| #436×C271 | 2 |
| #3354 | 271 |