Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
408 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31827015 | C2 | semidirect |
| 2. #31826999 | C2 | semidirect |
| 3. #31826874 | C2 | semidirect |
| 4. #31826854 | C2 | semidirect |
| 5. #31826830 | C2 | semidirect |
| 6. #31826825 | C2 | semidirect |
| 7. #31826718 | C2 | semidirect |
| 8. #31826711 | C2 | semidirect |
| 9. C4×#17985381 | C2 | semidirect |
| 10. C4×D2264 | C2 | semidirect |
| 11. C4×M16×C283 | C2 | semidirect |
| 110. C8×C283 | #41 | semidirect |
| 137. C283 | #3171 | semidirect |
| 149. C4×M16 | D283 | semidirect |
| 248. C8 | #17985392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827015 | 2 |
| #31826999 | 2 |
| #31826874 | 2 |
| #31826854 | 2 |
| #31826830 | 2 |
| #31826825 | 2 |
| #31826718 | 2 |
| #31826711 | 2 |
| C4×#17985381 | 2 |
| C4×D2264 | 2 |
| C4×M16×C283 | 2 |
| #3171 | 283 |