Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 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. #31827022 | C2 | semidirect |
| 5. #31826236 | C2 | semidirect |
| 6. #31826221 | C2 | semidirect |
| 7. #339×C283 | C2 | semidirect |
| 28. C2×Dic566 | Q8 | semidirect |
| 29. C2×D1132 | Q8 | semidirect |
| 101. C283 | #2031 | semidirect |
| 108. #339 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827022 | 2 |
| #31826481 | 2 |
| C2×#22583538 | 2 |
| #31826438 | 2 |
| #31826236 | 2 |
| #31826221 | 2 |
| #339×C283 | 2 |
| #2031 | 283 |