Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 184 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 |
|---|---|---|
| 2. #31826665 | C2 | semidirect |
| 3. #31826596 | C2 | semidirect |
| 4. #31826215 | C2 | semidirect |
| 5. #31826209 | C2 | semidirect |
| 6. #31826208 | C2 | semidirect |
| 7. #460×C283 | C2 | semidirect |
| 52. C283⋊C8 | SD16 | semidirect |
| 86. C283 | #1688 | semidirect |
| 90. #460 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826841 | 2 |
| #31826665 | 2 |
| #31826596 | 2 |
| #31826215 | 2 |
| #31826209 | 2 |
| #31826208 | 2 |
| #460×C283 | 2 |
| #1688 | 283 |