Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 2. #41×Dic271 | C2 | semidirect |
| 3. #31773913 | C2 | semidirect |
| 4. C2×#22576086 | C2 | semidirect |
| 5. #568×C271 | C2 | semidirect |
| 7. #22576207 | C4 | semidirect |
| 8. #22576206 | C4 | semidirect |
| 14. #22576119 | C22 | semidirect |
| 15. C2×C4×Dic271 | C22 | semidirect |
| 16. #22576086 | C22 | semidirect |
| 17. #22576086 | C22 | semidirect |
| 20. C2×M16×C271 | C22 | semidirect |
| 24. #16864654 | C2×C4 | semidirect |
| 27. C2×Dic542 | C2×C4 | semidirect |
| 29. C2×D1084 | C2×C4 | semidirect |
| 83. C271 | #2901 | semidirect |
| 86. #568 | D271 | semidirect |
| 98. C2×M16 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774733 | 2 |
| #41×Dic271 | 2 |
| #31773913 | 2 |
| C2×#22576086 | 2 |
| #568×C271 | 2 |
| #2901 | 271 |