Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic542 | C2 | semidirect |
| 2. C2×#22576190 | C2 | semidirect |
| 3. #31774052 | C2 | semidirect |
| 4. #31774035 | C2 | semidirect |
| 5. #31773905 | C2 | semidirect |
| 6. #31773861 | C2 | semidirect |
| 15. C2×#16864644 | C22 | semidirect |
| 16. C2×#16864642 | C22 | semidirect |
| 18. #22576083 | C22 | semidirect |
| 34. C2×Dic542 | D4 | semidirect |
| 95. C22×C271 | #137 | semidirect |
| 108. C271 | #3004 | semidirect |
| 204. C22 | #22576190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic542 | 2 |
| C2×#22576190 | 2 |
| #31774052 | 2 |
| #31774035 | 2 |
| #31773905 | 2 |
| #31773861 | 2 |
| #525×C271 | 2 |
| #3004 | 271 |