Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 2. #31826869 | C2 | semidirect |
| 3. #31826843 | C2 | semidirect |
| 4. #31826814 | C2 | semidirect |
| 7. Q16×Dic283 | C2 | semidirect |
| 8. #31826559 | C2 | semidirect |
| 9. #31826557 | C2 | semidirect |
| 77. C2×Dic283 | Q16 | semidirect |
| 114. C283 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827017 | 2 |
| #31826869 | 2 |
| #31826843 | 2 |
| #31826814 | 2 |
| #31826706 | 2 |
| #31826704 | 2 |
| Q16×Dic283 | 2 |
| #31826559 | 2 |
| #31826557 | 2 |
| C2×C8×Dic283 | 2 |
| #467×C283 | 2 |
| #3170 | 283 |