Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
168 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 63 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. #31826596 | C2 | semidirect |
| 4. #31826215 | C2 | semidirect |
| 6. #31826187 | C2 | semidirect |
| 7. Q8⋊C8×C283 | C2 | semidirect |
| 51. C283⋊C8 | SD16 | semidirect |
| 77. C283 | #1582 | semidirect |
| 83. Q8⋊C8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826596 | 2 |
| C4×#17985379 | 2 |
| #31826530 | 2 |
| #31826215 | 2 |
| #31826194 | 2 |
| #31826187 | 2 |
| Q8⋊C8×C283 | 2 |
| #1582 | 283 |