Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#22583568 | C2 | semidirect |
| 3. C2×#22583532 | C2 | semidirect |
| 4. C2×#22583530 | C2 | semidirect |
| 5. C2×(C2×D283)⋊C8 | C2 | semidirect |
| 6. #31826227 | C2 | semidirect |
| 7. #340×C283 | C2 | semidirect |
| 13. #22583585 | C4 | semidirect |
| 49. C4⋊Dic283 | D4 | semidirect |
| 62. C4⋊C4×C283 | D4 | semidirect |
| 145. C283 | #1875 | semidirect |
| 153. #340 | D283 | semidirect |
| 205. C4⋊C4 | D1132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583585 | 2 |
| C2×#22583568 | 2 |
| C2×#22583532 | 2 |
| C2×#22583530 | 2 |
| C2×(C2×D283)⋊C8 | 2 |
| #31826227 | 2 |
| #340×C283 | 2 |
| #1875 | 283 |