Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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. #31827071 | C2 | direct (N × H) |
| 2. C2×#22583607 | C2 | semidirect |
| 3. C2×#22583595 | C2 | semidirect |
| 4. C2×#22583585 | C2 | semidirect |
| 5. C2×#22583585 | C2 | semidirect |
| 6. C2×#22583572 | C2 | semidirect |
| 7. C2×#22583567 | C2 | semidirect |
| 8. C2×#125×C283 | C2 | semidirect |
| 14. #22583607 | C22 | semidirect |
| 15. #22583595 | C22 | semidirect |
| 16. #22583585 | C22 | semidirect |
| 17. #22583585 | C22 | semidirect |
| 18. #22583572 | C22 | semidirect |
| 19. #22583567 | C22 | semidirect |
| 25. #125×C283 | C22 | semidirect |
| 92. C2×C283 | #540 | semidirect |
| 97. C283 | C2×#540 | semidirect |
| 101. C2×#125 | D283 | semidirect |
| 113. #125 | C2×D283 | semidirect |
| 192. C2 | #31827071 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827071 | 2 |
| C2×#22583607 | 2 |
| C2×#22583595 | 2 |
| C2×#22583585 | 2 |
| C2×#22583572 | 2 |
| C2×#22583567 | 2 |
| C2×#125×C283 | 2 |
| C2×#540 | 283 |