Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 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. #31827093 | C2 | semidirect |
| 3. #31826771 | C2 | semidirect |
| 4. #31826768 | C2 | semidirect |
| 5. #31826754 | C2 | semidirect |
| 6. #31826749 | C2 | semidirect |
| 7. C2×#22583541 | C2 | semidirect |
| 8. #31826493 | C2 | semidirect |
| 11. #428×C283 | C2 | semidirect |
| 42. #17985392 | Q8 | semidirect |
| 123. C283 | #3084 | semidirect |
| 131. #428 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827093 | 2 |
| #31826946 | 2 |
| #31826771 | 2 |
| #31826768 | 2 |
| #31826754 | 2 |
| #31826749 | 2 |
| C2×#22583541 | 2 |
| #31826493 | 2 |
| #31826467 | 2 |
| #31826459 | 2 |
| #428×C283 | 2 |
| #3084 | 283 |