Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31827195 | C2 | semidirect |
| 3. #31826810 | C2 | semidirect |
| 4. #31826753 | C2 | semidirect |
| 5. #31826752 | C2 | semidirect |
| 6. #31826664 | C2 | semidirect |
| 7. #31826662 | C2 | semidirect |
| 8. C8×Dic566 | C2 | semidirect |
| 9. #31826556 | C2 | semidirect |
| 10. C4×#17985381 | C2 | semidirect |
| 11. #486×C283 | C2 | semidirect |
| 77. Dic566 | SD16 | semidirect |
| 78. Dic566 | #41 | semidirect |
| 125. C283 | #3362 | semidirect |
| 130. #486 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827195 | 2 |
| #31827135 | 2 |
| #31826810 | 2 |
| #31826753 | 2 |
| #31826752 | 2 |
| #31826664 | 2 |
| #31826662 | 2 |
| C8×Dic566 | 2 |
| #31826556 | 2 |
| C4×#17985381 | 2 |
| #486×C283 | 2 |
| #3362 | 283 |