Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 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×#22583601 | C2 | semidirect |
| 3. #31826775 | C2 | semidirect |
| 4. #31826771 | C2 | semidirect |
| 5. #31826768 | C2 | semidirect |
| 6. #31826764 | C2 | semidirect |
| 7. #31826508 | C2 | semidirect |
| 8. #31826488 | C2 | semidirect |
| 11. #428×C283 | C2 | semidirect |
| 135. C283 | #3080 | semidirect |
| 144. #428 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583601 | 2 |
| #31826933 | 2 |
| #31826775 | 2 |
| #31826771 | 2 |
| #31826768 | 2 |
| #31826764 | 2 |
| #31826508 | 2 |
| #31826488 | 2 |
| #31826467 | 2 |
| #31826464 | 2 |
| #428×C283 | 2 |
| #3080 | 283 |