Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 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. #31774634 | C2 | direct (N × H) |
| 2. C2×#22576154 | C2 | semidirect |
| 3. C2×#22576141 | C2 | semidirect |
| 4. C2×#22576132 | C2 | semidirect |
| 5. C2×#22576128 | C2 | semidirect |
| 6. C2×#127×C271 | C2 | semidirect |
| 9. C23×Dic271 | C22 | semidirect |
| 10. #22576154 | C22 | semidirect |
| 11. #22576141 | C22 | semidirect |
| 12. #22576132 | C22 | semidirect |
| 13. #22576128 | C22 | semidirect |
| 14. C2×Dic271⋊C4 | C22 | semidirect |
| 16. C2×C22⋊Dic271 | C22 | semidirect |
| 19. C22×D4×C271 | C22 | semidirect |
| 20. #127×C271 | C22 | semidirect |
| 21. C2×C42×C271 | C22 | semidirect |
| 29. C22×Dic271 | C23 | semidirect |
| 30. Dic271⋊C4 | C23 | semidirect |
| 32. C22⋊Dic271 | C23 | semidirect |
| 39. C2×D4×C271 | C23 | semidirect |
| 41. C42×C271 | C23 | semidirect |
| 74. C2×C271 | #560 | semidirect |
| 77. C271 | C2×#560 | semidirect |
| 80. C2×#127 | D271 | semidirect |
| 88. C22×D4 | C2×D271 | semidirect |
| 90. #127 | C2×D271 | semidirect |
| 99. C2×C42 | C2×D271 | semidirect |
| 110. C2×D4 | C22×D271 | semidirect |
| 119. C42 | C22×D271 | semidirect |
| 153. C2 | #31774634 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774634 | 2 |
| C2×#22576154 | 2 |
| C2×#22576141 | 2 |
| C2×#22576132 | 2 |
| C2×#22576128 | 2 |
| C2×#127×C271 | 2 |
| C2×#560 | 271 |