Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31827189 | C2 | semidirect |
| 2. #31827176 | C2 | semidirect |
| 3. #31826821 | C2 | semidirect |
| 4. #31826774 | C2 | semidirect |
| 5. #31826752 | C2 | semidirect |
| 7. #31826667 | C2 | semidirect |
| 8. C8×Dic566 | C2 | semidirect |
| 9. #31826550 | C2 | semidirect |
| 11. #487×C283 | C2 | semidirect |
| 120. C283 | #3360 | semidirect |
| 125. #487 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827189 | 2 |
| #31827176 | 2 |
| #31826821 | 2 |
| #31826774 | 2 |
| #31826752 | 2 |
| #31826683 | 2 |
| #31826667 | 2 |
| C8×Dic566 | 2 |
| #31826550 | 2 |
| C4×D2264 | 2 |
| #487×C283 | 2 |
| #3360 | 283 |