Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 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. #31827201 | C2 | semidirect |
| 2. #31827200 | C2 | semidirect |
| 3. #31826846 | C2 | semidirect |
| 5. #31826682 | C2 | semidirect |
| 6. #31826679 | C2 | semidirect |
| 7. #31826666 | C2 | semidirect |
| 8. #31826589 | C2 | semidirect |
| 9. C4×#17985382 | C2 | semidirect |
| 10. #31826545 | C2 | semidirect |
| 11. #460×C283 | C2 | semidirect |
| 127. C283 | #3396 | semidirect |
| 136. #460 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827201 | 2 |
| #31827200 | 2 |
| #31826846 | 2 |
| #31826841 | 2 |
| #31826682 | 2 |
| #31826679 | 2 |
| #31826666 | 2 |
| #31826589 | 2 |
| C4×#17985382 | 2 |
| #31826545 | 2 |
| #460×C283 | 2 |
| #3396 | 283 |