Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22576186 | C2 | semidirect |
| 2. C4×#16864654 | C2 | semidirect |
| 3. #31774094 | C2 | semidirect |
| 4. #31774089 | C2 | semidirect |
| 5. #31773921 | C2 | semidirect |
| 6. #31773902 | C2 | semidirect |
| 7. C2×#127×C271 | C2 | semidirect |
| 10. C2×#16864642 | C22 | semidirect |
| 11. C2×#16864639 | C22 | semidirect |
| 13. C4×Dic542 | C22 | semidirect |
| 14. C4×D1084 | C22 | semidirect |
| 19. C4⋊(C271⋊C8) | C22 | semidirect |
| 20. #22576081 | C22 | semidirect |
| 28. #16864654 | D4 | semidirect |
| 59. Dic542 | C2×D4 | semidirect |
| 61. D1084 | C2×D4 | semidirect |
| 94. C4×C271 | AGL(1,ℤ/8) | semidirect |
| 104. C271 | #3038 | semidirect |
| 107. C2×#127 | D271 | semidirect |
| 201. C4 | #22576186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576186 | 2 |
| C4×#16864654 | 2 |
| #31774094 | 2 |
| #31774089 | 2 |
| #31773921 | 2 |
| #31773902 | 2 |
| C2×#127×C271 | 2 |
| #3038 | 271 |