Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#22583639 | C2 | semidirect |
| 2. Q8×D1132 | C2 | semidirect |
| 4. #31826845 | C2 | semidirect |
| 5. #31826724 | C2 | semidirect |
| 6. #31826675 | C2 | semidirect |
| 7. #31826670 | C2 | semidirect |
| 8. #31826628 | C2 | semidirect |
| 9. #31826622 | C2 | semidirect |
| 10. #31826544 | C2 | semidirect |
| 11. C4×SD16×C283 | C2 | semidirect |
| 73. SD16×C283 | D4 | semidirect |
| 123. C4×C283 | #137 | semidirect |
| 134. C283 | #3276 | semidirect |
| 145. C4×SD16 | D283 | semidirect |
| 196. SD16 | D1132 | semidirect |
| 261. C4 | #22583639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583639 | 2 |
| Q8×D1132 | 2 |
| #31827119 | 2 |
| #31826845 | 2 |
| #31826724 | 2 |
| #31826675 | 2 |
| #31826670 | 2 |
| #31826628 | 2 |
| #31826622 | 2 |
| #31826544 | 2 |
| C4×SD16×C283 | 2 |
| #3276 | 283 |