Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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. #31827282 | C2 | semidirect |
| 2. #31826903 | C2 | semidirect |
| 3. C2×#22583555 | C2 | semidirect |
| 4. #31826735 | C2 | semidirect |
| 5. #31826282 | C2 | semidirect |
| 6. #31826273 | C2 | semidirect |
| 7. #350×C283 | C2 | semidirect |
| 90. C283 | #2193 | semidirect |
| 98. #350 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827282 | 2 |
| #31826903 | 2 |
| C2×#22583555 | 2 |
| #31826735 | 2 |
| #31826282 | 2 |
| #31826273 | 2 |
| #350×C283 | 2 |
| #2193 | 283 |