Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
136 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 136 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. #31826867 | C2 | semidirect |
| 2. #31826292 | C2 | semidirect |
| 3. #31826290 | C2 | semidirect |
| 4. C4⋊(C283⋊C16) | C2 | semidirect |
| 62. C283 | #2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826867 | 2 |
| #31826292 | 2 |
| #31826290 | 2 |
| C4⋊(C283⋊C16) | 2 |
| #31826266 | 2 |
| C4×D8×C283 | 2 |
| #2228 | 283 |