Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 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. C22×#17985392 | C2 | semidirect |
| 2. C2×#22583638 | C2 | semidirect |
| 3. C2×#22583584 | C2 | semidirect |
| 4. #31826612 | C2 | semidirect |
| 5. #31826606 | C2 | semidirect |
| 6. #31826601 | C2 | semidirect |
| 7. #31826467 | C2 | semidirect |
| 8. #407×C283 | C2 | semidirect |
| 13. C2×#17985392 | C22 | semidirect |
| 14. C22×Dic566 | C22 | semidirect |
| 15. C22×D1132 | C22 | semidirect |
| 16. C22×D1132 | C22 | semidirect |
| 21. C2×#17985381 | C22 | semidirect |
| 22. C2×D2264 | C22 | semidirect |
| 26. #22583584 | C22 | semidirect |
| 27. C2×C4⋊Dic283 | C22 | semidirect |
| 29. #22583535 | C22 | semidirect |
| 30. #22583532 | C22 | semidirect |
| 32. C2×M16×C283 | C22 | semidirect |
| 33. C22⋊C8×C283 | C22 | semidirect |
| 34. C22⋊C8×C283 | C22 | semidirect |
| 42. #17985392 | D4 | semidirect |
| 89. Dic566 | C2×D4 | semidirect |
| 94. D1132 | C2×D4 | semidirect |
| 131. C22×C283 | AGL(1,ℤ/8) | semidirect |
| 155. C283 | #3006 | semidirect |
| 164. #407 | D283 | semidirect |
| 180. C2×M16 | C2×D283 | semidirect |
| 189. C22⋊C8 | C2×D283 | semidirect |
| 190. C22⋊C8 | C2×D283 | semidirect |
| 295. C22 | #22583638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985392 | 2 |
| C2×#22583638 | 2 |
| C2×#22583584 | 2 |
| #31826612 | 2 |
| #31826606 | 2 |
| #31826601 | 2 |
| #31826467 | 2 |
| #407×C283 | 2 |
| #3006 | 283 |