Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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. #31826844 | C2 | semidirect |
| 3. #31826813 | C2 | semidirect |
| 4. #31826812 | C2 | semidirect |
| 5. #31826811 | C2 | semidirect |
| 6. C8×C283⋊C8 | C2 | semidirect |
| 7. #486×C283 | C2 | semidirect |
| 74. C283 | #1709 | semidirect |
| 81. #486 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826844 | 2 |
| #31826841 | 2 |
| #31826813 | 2 |
| #31826812 | 2 |
| #31826811 | 2 |
| C8×C283⋊C8 | 2 |
| #486×C283 | 2 |
| #1709 | 283 |