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. #31827096 | C2 | semidirect |
| 3. #31826775 | C2 | semidirect |
| 4. #31826764 | C2 | semidirect |
| 5. #31826754 | C2 | semidirect |
| 6. #31826749 | C2 | semidirect |
| 7. #31826505 | C2 | semidirect |
| 8. #31826491 | C2 | semidirect |
| 11. C2×#106×C283 | C2 | semidirect |
| 42. #17985392 | Q8 | semidirect |
| 123. C283 | #3084 | semidirect |
| 132. C2×#106 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827096 | 2 |
| #31826946 | 2 |
| #31826775 | 2 |
| #31826764 | 2 |
| #31826754 | 2 |
| #31826749 | 2 |
| #31826505 | 2 |
| #31826491 | 2 |
| #31826464 | 2 |
| #31826462 | 2 |
| C2×#106×C283 | 2 |
| #3084 | 283 |