Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31774447 | C2 | semidirect |
| 2. #31774215 | C2 | semidirect |
| 3. #31774187 | C2 | semidirect |
| 4. #31774092 | C2 | semidirect |
| 5. #31774031 | C2 | semidirect |
| 6. #31774007 | C2 | semidirect |
| 7. #31773954 | C2 | semidirect |
| 8. C2×C4×D4×C271 | C2 | semidirect |
| 11. #22576160 | C22 | semidirect |
| 12. #22576157 | C22 | semidirect |
| 17. C4×D1084 | C22 | semidirect |
| 18. #22576091 | C22 | semidirect |
| 19. C4⋊(C271⋊C8) | C22 | semidirect |
| 21. #22576080 | C22 | semidirect |
| 23. #22576071 | C22 | semidirect |
| 81. D4×C271 | #41 | semidirect |
| 120. C271 | #3109 | semidirect |
| 123. C2×C4×D4 | D271 | semidirect |
| 199. D4 | #16864654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774447 | 2 |
| #31774215 | 2 |
| #31774187 | 2 |
| #31774092 | 2 |
| #31774031 | 2 |
| #31774007 | 2 |
| #31773954 | 2 |
| C2×C4×D4×C271 | 2 |
| #3109 | 271 |