Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #31827265 | C2 | semidirect |
| 2. C2×#22583636 | C2 | semidirect |
| 3. #31827032 | C2 | semidirect |
| 4. #31826483 | C2 | semidirect |
| 5. #31826438 | C2 | semidirect |
| 6. #31826236 | C2 | semidirect |
| 7. #418×C283 | C2 | semidirect |
| 40. C2×Dic566 | D4 | semidirect |
| 42. C2×D1132 | D4 | semidirect |
| 55. #17985376 | D4 | semidirect |
| 71. C2×C8×C283 | D4 | semidirect |
| 142. C283 | #2008 | semidirect |
| 148. #418 | D283 | semidirect |
| 210. C2×C8 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827265 | 2 |
| C2×#22583636 | 2 |
| #31827032 | 2 |
| #31826483 | 2 |
| #31826438 | 2 |
| #31826236 | 2 |
| #418×C283 | 2 |
| #2008 | 283 |