Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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. #31827180 | C2 | semidirect |
| 2. #31826815 | C2 | semidirect |
| 3. #31826803 | C2 | semidirect |
| 4. #31826755 | C2 | semidirect |
| 5. #31826696 | C2 | semidirect |
| 6. #31826667 | C2 | semidirect |
| 7. #31826610 | C2 | semidirect |
| 8. C4×#17985377 | C2 | semidirect |
| 9. D4×C283⋊C8 | C2 | semidirect |
| 10. #31826461 | C2 | semidirect |
| 11. #547×C283 | C2 | semidirect |
| 130. C283 | #3303 | semidirect |
| 133. #547 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827180 | 2 |
| #31826815 | 2 |
| #31826803 | 2 |
| #31826755 | 2 |
| #31826696 | 2 |
| #31826667 | 2 |
| #31826610 | 2 |
| C4×#17985377 | 2 |
| D4×C283⋊C8 | 2 |
| #31826461 | 2 |
| #547×C283 | 2 |
| #3303 | 283 |