Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31827266 | C2 | semidirect |
| 2. #31826732 | C2 | semidirect |
| 3. #31826632 | C2 | semidirect |
| 4. #31826583 | C2 | semidirect |
| 5. #493×C283 | C2 | semidirect |
| 6. #22583655 | C22 | semidirect |
| 7. #22583636 | C22 | semidirect |
| 12. #22583616 | C22 | semidirect |
| 13. #22583546 | C22 | semidirect |
| 14. #22583538 | C22 | semidirect |
| 15. #22583527 | C22 | semidirect |
| 16. C2×D8×C283 | C22 | semidirect |
| 17. #127×C283 | C22 | semidirect |
| 18. C4×C8×C283 | C22 | semidirect |
| 23. Dic1132 | D4 | semidirect |
| 24. #17985381 | D4 | semidirect |
| 26. D2264 | D4 | semidirect |
| 64. C283 | #3292 | semidirect |
| 67. #493 | D283 | semidirect |
| 77. C2×D8 | C2×D283 | semidirect |
| 79. #127 | C2×D283 | semidirect |
| 83. C4×C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827266 | 2 |
| #31826732 | 2 |
| #31826632 | 2 |
| #31826583 | 2 |
| #493×C283 | 2 |
| #3292 | 283 |