Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #31826807 | C2 | direct (N × H) |
| 4. C2×#22583544 | C2 | semidirect |
| 5. C2×#22583542 | C2 | semidirect |
| 6. C2×#22583535 | C2 | semidirect |
| 7. C2×#22583535 | C2 | semidirect |
| 21. #22583544 | C22 | semidirect |
| 22. #22583542 | C22 | semidirect |
| 23. #22583535 | C22 | semidirect |
| 24. #22583535 | C22 | semidirect |
| 102. C2×C283 | #485 | semidirect |
| 106. C283 | C2×#485 | semidirect |
| 209. C2 | #31826807 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583589 | 2 |
| C2×#22583569 | 2 |
| #31826807 | 2 |
| C2×#22583544 | 2 |
| C2×#22583542 | 2 |
| C2×#22583535 | 2 |
| C2×C22⋊C8×C283 | 2 |
| C2×#485 | 283 |