Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
424 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. C2×#22583575 | C2 | semidirect |
| 3. #31826778 | C2 | semidirect |
| 4. #31826759 | C2 | semidirect |
| 5. #31826664 | C2 | semidirect |
| 6. #31826606 | C2 | semidirect |
| 7. #31826603 | C2 | semidirect |
| 8. #31826564 | C2 | semidirect |
| 9. #31826562 | C2 | semidirect |
| 10. #31826519 | C2 | semidirect |
| 11. #480×C283 | C2 | semidirect |
| 86. Dic566 | #41 | semidirect |
| 140. C283 | #3112 | semidirect |
| 145. #480 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827010 | 2 |
| C2×#22583575 | 2 |
| #31826778 | 2 |
| #31826759 | 2 |
| #31826664 | 2 |
| #31826606 | 2 |
| #31826603 | 2 |
| #31826564 | 2 |
| #31826562 | 2 |
| #31826519 | 2 |
| #480×C283 | 2 |
| #3112 | 283 |