Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#22576167 | C2 | semidirect |
| 2. #31774019 | C2 | semidirect |
| 3. #31774014 | C2 | semidirect |
| 4. #31773946 | C2 | semidirect |
| 5. #31773914 | C2 | semidirect |
| 6. #31773855 | C2 | semidirect |
| 10. #22576167 | C22 | semidirect |
| 11. #22576167 | C22 | semidirect |
| 17. #22576096 | C22 | semidirect |
| 18. #22576087 | C22 | semidirect |
| 19. #22576070 | C22 | semidirect |
| 20. C8×Dic271 | C22 | semidirect |
| 22. #137×C271 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C271 | C4 | semidirect |
| 89. C271 | #2955 | semidirect |
| 99. #137 | Dic271 | semidirect |
| 100. AGL(1,ℤ/8) | Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576167 | 2 |
| #31774019 | 2 |
| #31774014 | 2 |
| #31773946 | 2 |
| #31773914 | 2 |
| #31773855 | 2 |
| #575×C271 | 2 |
| #2955 | 271 |