Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31827002 | C2 | semidirect |
| 2. #31826866 | C2 | semidirect |
| 3. #31826850 | C2 | semidirect |
| 4. #31826821 | C2 | semidirect |
| 5. #31826703 | C2 | semidirect |
| 7. #31826697 | C2 | semidirect |
| 8. C4×#17985379 | C2 | semidirect |
| 9. C4×D2264 | C2 | semidirect |
| 10. C4×C8×D283 | C2 | semidirect |
| 11. C4×Q16×C283 | C2 | semidirect |
| 118. C283 | #3168 | semidirect |
| 127. C4×Q16 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827002 | 2 |
| #31826866 | 2 |
| #31826850 | 2 |
| #31826821 | 2 |
| #31826703 | 2 |
| #31826702 | 2 |
| #31826697 | 2 |
| C4×#17985379 | 2 |
| C4×D2264 | 2 |
| C4×C8×D283 | 2 |
| C4×Q16×C283 | 2 |
| #3168 | 283 |