Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#17985380 | C2 | semidirect |
| 3. #31826942 | C2 | semidirect |
| 4. #31826684 | C2 | semidirect |
| 5. #31826662 | C2 | semidirect |
| 6. #31826492 | C2 | semidirect |
| 7. #31826470 | C2 | semidirect |
| 8. #31826461 | C2 | semidirect |
| 12. C2×#17985382 | C22 | semidirect |
| 15. C2×#17985380 | C22 | semidirect |
| 18. C4×Dic566 | C22 | semidirect |
| 22. C4⋊(C283⋊C8) | C22 | semidirect |
| 23. #22583534 | C22 | semidirect |
| 25. #22583531 | C22 | semidirect |
| 35. C2×Dic566 | D4 | semidirect |
| 116. C283 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583640 | 2 |
| C22×#17985380 | 2 |
| #31826942 | 2 |
| #31826684 | 2 |
| #31826662 | 2 |
| #31826492 | 2 |
| #31826470 | 2 |
| #31826461 | 2 |
| #535×C283 | 2 |
| #3043 | 283 |