Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#22583632 | C2 | semidirect |
| 2. C2×#22583630 | C2 | semidirect |
| 3. #31827011 | C2 | semidirect |
| 4. #31826850 | C2 | semidirect |
| 5. #31826848 | C2 | semidirect |
| 6. #31826846 | C2 | semidirect |
| 7. #31826843 | C2 | semidirect |
| 8. #31826840 | C2 | semidirect |
| 9. #31826836 | C2 | semidirect |
| 10. C2×C8×Dic283 | C2 | semidirect |
| 11. C2×#135×C283 | C2 | semidirect |
| 55. C2×C283⋊C8 | D4 | semidirect |
| 74. C2×C8×C283 | D4 | semidirect |
| 119. Dic283 | #135 | semidirect |
| 125. C283 | #3147 | semidirect |
| 129. C2×#135 | D283 | semidirect |
| 194. C2×C8 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583632 | 2 |
| C2×#22583630 | 2 |
| #31827011 | 2 |
| #31826850 | 2 |
| #31826848 | 2 |
| #31826846 | 2 |
| #31826843 | 2 |
| #31826840 | 2 |
| #31826836 | 2 |
| C2×C8×Dic283 | 2 |
| C2×#135×C283 | 2 |
| #3147 | 283 |