Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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. #31826816 | C2 | semidirect |
| 5. #31826212 | C2 | semidirect |
| 6. #31826210 | C2 | semidirect |
| 7. #334×C283 | C2 | semidirect |
| 77. C283 | #1679 | semidirect |
| 83. #334 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826816 | 2 |
| #31826746 | 2 |
| #31826671 | 2 |
| C8×D1132 | 2 |
| #31826212 | 2 |
| #31826210 | 2 |
| #334×C283 | 2 |
| #1679 | 283 |