Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
224 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 12. #22583545 | C4 | semidirect |
| 13. #22583543 | C4 | semidirect |
| 14. #22583541 | C4 | semidirect |
| 16. #22583520 | C4 | semidirect |
| 79. C283 | #1773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583545 | 2 |
| #31826501 | 2 |
| #31826420 | 2 |
| C2×#22583520 | 2 |
| #31826226 | 2 |
| #31826224 | 2 |
| #405×C283 | 2 |
| #1773 | 283 |