Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#22583641 | C2 | semidirect |
| 3. C4×#17985392 | C2 | semidirect |
| 4. #31826684 | C2 | semidirect |
| 5. #31826677 | C2 | semidirect |
| 6. #31826489 | C2 | semidirect |
| 7. #31826474 | C2 | semidirect |
| 8. #31826470 | C2 | semidirect |
| 9. C2×#124×C283 | C2 | semidirect |
| 13. C2×#17985382 | C22 | semidirect |
| 15. C2×#17985379 | C22 | semidirect |
| 19. C4×Dic566 | C22 | semidirect |
| 20. C4×D1132 | C22 | semidirect |
| 25. C4⋊(C283⋊C8) | C22 | semidirect |
| 26. #22583534 | C22 | semidirect |
| 125. C283 | #3040 | semidirect |
| 129. C2×#124 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583641 | 2 |
| C2×#22583636 | 2 |
| C4×#17985392 | 2 |
| #31826684 | 2 |
| #31826677 | 2 |
| #31826489 | 2 |
| #31826474 | 2 |
| #31826470 | 2 |
| C2×#124×C283 | 2 |
| #3040 | 283 |