Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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. #31826521 | C2 | semidirect |
| 3. #31826516 | C2 | semidirect |
| 4. Q8⋊(C283⋊C8) | C2 | semidirect |
| 5. #31826194 | C2 | semidirect |
| 6. #31826192 | C2 | semidirect |
| 7. Q8⋊C8×C283 | C2 | semidirect |
| 108. C283 | #1488 | semidirect |
| 114. Q8⋊C8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#17985393 | 2 |
| #31826521 | 2 |
| #31826516 | 2 |
| Q8⋊(C283⋊C8) | 2 |
| #31826194 | 2 |
| #31826192 | 2 |
| Q8⋊C8×C283 | 2 |
| #1488 | 283 |