Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 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. #31826841 | C2 | semidirect |
| 2. #31826660 | C2 | semidirect |
| 3. #31826543 | C2 | semidirect |
| 4. #31826215 | C2 | semidirect |
| 5. #31826209 | C2 | semidirect |
| 6. #31826208 | C2 | semidirect |
| 7. #459×C283 | C2 | semidirect |
| 53. C283⋊C8 | D8 | semidirect |
| 92. C283 | #1687 | semidirect |
| 96. #459 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826841 | 2 |
| #31826660 | 2 |
| #31826543 | 2 |
| #31826215 | 2 |
| #31826209 | 2 |
| #31826208 | 2 |
| #459×C283 | 2 |
| #1687 | 283 |