Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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. #31774501 | C2 | direct (N × H) |
| 2. C2×#22576152 | C2 | semidirect |
| 3. C2×#22576141 | C2 | semidirect |
| 4. C2×#22576132 | C2 | semidirect |
| 5. C2×#22576131 | C2 | semidirect |
| 6. C2×D4×Dic271 | C2 | semidirect |
| 7. C2×#22576117 | C2 | semidirect |
| 8. C2×#127×C271 | C2 | semidirect |
| 12. #22576152 | C22 | semidirect |
| 13. #22576141 | C22 | semidirect |
| 14. #22576132 | C22 | semidirect |
| 15. #22576131 | C22 | semidirect |
| 16. D4×Dic271 | C22 | semidirect |
| 17. #22576117 | C22 | semidirect |
| 27. #127×C271 | C22 | semidirect |
| 93. C2×C271 | #540 | semidirect |
| 97. C271 | C2×#540 | semidirect |
| 100. C2×#127 | D271 | semidirect |
| 112. #127 | C2×D271 | semidirect |
| 192. C2 | #31774501 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774501 | 2 |
| C2×#22576152 | 2 |
| C2×#22576141 | 2 |
| C2×#22576132 | 2 |
| C2×#22576131 | 2 |
| C2×D4×Dic271 | 2 |
| C2×#22576117 | 2 |
| C2×#127×C271 | 2 |
| C2×#540 | 271 |