Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31826501 | C2 | semidirect |
| 3. #31826481 | C2 | semidirect |
| 4. #31826439 | C2 | semidirect |
| 5. #31826438 | C2 | semidirect |
| 6. #31826423 | C2 | semidirect |
| 7. #421×C283 | C2 | semidirect |
| 13. C2×#17985382 | C4 | semidirect |
| 14. C2×#17985380 | C4 | semidirect |
| 15. C2×#17985379 | C4 | semidirect |
| 16. C2×#17985377 | C4 | semidirect |
| 132. C283 | #1976 | semidirect |
| 137. #421 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583630 | 2 |
| #31826501 | 2 |
| #31826481 | 2 |
| #31826439 | 2 |
| #31826438 | 2 |
| #31826423 | 2 |
| #421×C283 | 2 |
| #1976 | 283 |