Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774698 | C2 | semidirect |
| 2. #31774164 | C2 | semidirect |
| 3. #31774064 | C2 | semidirect |
| 4. #31774015 | C2 | semidirect |
| 5. #493×C271 | C2 | semidirect |
| 6. #22576205 | C22 | semidirect |
| 7. #22576186 | C22 | semidirect |
| 12. #22576166 | C22 | semidirect |
| 13. #22576096 | C22 | semidirect |
| 14. #22576088 | C22 | semidirect |
| 15. #22576077 | C22 | semidirect |
| 16. C2×D8×C271 | C22 | semidirect |
| 17. #127×C271 | C22 | semidirect |
| 18. C4×C8×C271 | C22 | semidirect |
| 23. Dic1084 | D4 | semidirect |
| 24. #16864643 | D4 | semidirect |
| 26. D2168 | D4 | semidirect |
| 64. C271 | #3292 | semidirect |
| 67. #493 | D271 | semidirect |
| 77. C2×D8 | C2×D271 | semidirect |
| 79. #127 | C2×D271 | semidirect |
| 83. C4×C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774698 | 2 |
| #31774164 | 2 |
| #31774064 | 2 |
| #31774015 | 2 |
| #493×C271 | 2 |
| #3292 | 271 |