Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. M32×D283 | C2 | semidirect |
| 3. #31826500 | C2 | semidirect |
| 4. #31826276 | C2 | semidirect |
| 5. #31826275 | C2 | semidirect |
| 6. #31826274 | C2 | semidirect |
| 7. #360×C283 | C2 | semidirect |
| 9. #22583633 | C4 | semidirect |
| 13. #22583629 | C4 | semidirect |
| 14. Q16×D283 | C4 | semidirect |
| 16. D8×D283 | C4 | semidirect |
| 19. #22583550 | C22 | semidirect |
| 23. #22583542 | C22 | semidirect |
| 25. M32×C283 | C22 | semidirect |
| 26. #106×C283 | C22 | semidirect |
| 110. C283 | #2145 | semidirect |
| 118. #360 | D283 | semidirect |
| 133. M32 | C2×D283 | semidirect |
| 137. #106 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D283 | 2 |
| M32×D283 | 2 |
| #31826500 | 2 |
| #31826276 | 2 |
| #31826275 | 2 |
| #31826274 | 2 |
| #360×C283 | 2 |
| #2145 | 283 |