Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31827188 | C2 | semidirect |
| 2. #31826827 | C2 | semidirect |
| 3. #31826817 | C2 | semidirect |
| 4. #31826757 | C2 | semidirect |
| 5. #31826742 | C2 | semidirect |
| 7. #31826670 | C2 | semidirect |
| 8. #31826596 | C2 | semidirect |
| 9. #31826565 | C2 | semidirect |
| 11. D4×Q8×C283 | C2 | semidirect |
| 122. C283 | #3367 | semidirect |
| 125. D4×Q8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827188 | 2 |
| #31826827 | 2 |
| #31826817 | 2 |
| #31826757 | 2 |
| #31826742 | 2 |
| #31826680 | 2 |
| #31826670 | 2 |
| #31826596 | 2 |
| #31826565 | 2 |
| C4×#17985377 | 2 |
| D4×Q8×C283 | 2 |
| #3367 | 283 |