Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #31826832 | C2 | semidirect |
| 4. #31826817 | C2 | semidirect |
| 5. #31826816 | C2 | semidirect |
| 6. #31826815 | C2 | semidirect |
| 9. #487×C283 | C2 | semidirect |
| 106. C283 | #3139 | semidirect |
| 114. #487 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| C4⋊Q8×D283 | 2 |
| #31826832 | 2 |
| #31826817 | 2 |
| #31826816 | 2 |
| #31826815 | 2 |
| #31826472 | 2 |
| C4×#17985375 | 2 |
| #487×C283 | 2 |
| #3139 | 283 |