Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
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×#22583640 | C2 | semidirect |
| 2. C2×#22583589 | C2 | semidirect |
| 3. #31826627 | C2 | semidirect |
| 4. #31826621 | C2 | semidirect |
| 5. #31826616 | C2 | semidirect |
| 6. #31826466 | C2 | semidirect |
| 7. #31826429 | C2 | semidirect |
| 9. C22×Dic566 | C22 | semidirect |
| 11. C2×#17985382 | C22 | semidirect |
| 12. C2×#17985380 | C22 | semidirect |
| 13. C2×#17985376 | C22 | semidirect |
| 17. #22583589 | C22 | semidirect |
| 18. C2×C4⋊Dic283 | C22 | semidirect |
| 21. #22583534 | C22 | semidirect |
| 22. #22583531 | C22 | semidirect |
| 24. C22⋊(C283⋊C8) | C22 | semidirect |
| 130. C22×C283 | #137 | semidirect |
| 146. C283 | #3007 | semidirect |
| 277. C22 | #22583640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583640 | 2 |
| C2×#22583589 | 2 |
| #31826627 | 2 |
| #31826621 | 2 |
| #31826616 | 2 |
| #31826466 | 2 |
| #31826429 | 2 |
| C22×#41×C283 | 2 |
| #3007 | 283 |