Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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×#22576190 | C2 | semidirect |
| 2. C2×#22576139 | C2 | semidirect |
| 3. #31774059 | C2 | semidirect |
| 4. #31774053 | C2 | semidirect |
| 5. #31774048 | C2 | semidirect |
| 6. #31773898 | C2 | semidirect |
| 7. #31773861 | C2 | semidirect |
| 9. C22×Dic542 | C22 | semidirect |
| 11. C2×#16864644 | C22 | semidirect |
| 12. C2×#16864642 | C22 | semidirect |
| 13. C2×#16864638 | C22 | semidirect |
| 17. #22576139 | C22 | semidirect |
| 18. C2×C4⋊Dic271 | C22 | semidirect |
| 21. #22576084 | C22 | semidirect |
| 22. #22576081 | C22 | semidirect |
| 24. C22⋊(C271⋊C8) | C22 | semidirect |
| 130. C22×C271 | #137 | semidirect |
| 146. C271 | #3007 | semidirect |
| 277. C22 | #22576190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576190 | 2 |
| C2×#22576139 | 2 |
| #31774059 | 2 |
| #31774053 | 2 |
| #31774048 | 2 |
| #31773898 | 2 |
| #31773861 | 2 |
| C22×#41×C271 | 2 |
| #3007 | 271 |