Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #31826873 | C2 | semidirect |
| 4. #31826872 | C2 | semidirect |
| 5. #31826867 | C2 | semidirect |
| 6. #31826864 | C2 | semidirect |
| 7. #31826864 | C2 | semidirect |
| 11. #499×C283 | C2 | semidirect |
| 43. #17985375 | Q8 | semidirect |
| 44. #17985375 | Q8 | semidirect |
| 99. C283 | #3166 | semidirect |
| 108. #499 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827021 | 2 |
| #125×D283 | 2 |
| #31826873 | 2 |
| #31826872 | 2 |
| #31826867 | 2 |
| #31826864 | 2 |
| #31826506 | 2 |
| #31826504 | 2 |
| C4×#17985375 | 2 |
| #499×C283 | 2 |
| #3166 | 283 |