Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31827176 | C2 | semidirect |
| 3. #31826782 | C2 | semidirect |
| 4. #31826752 | C2 | semidirect |
| 5. #31826693 | C2 | semidirect |
| 6. #31826662 | C2 | semidirect |
| 7. #31826617 | C2 | semidirect |
| 8. C4×#17985381 | C2 | semidirect |
| 9. C8×D1132 | C2 | semidirect |
| 10. #102×D283 | C2 | semidirect |
| 11. #486×C283 | C2 | semidirect |
| 15. C2×#17985380 | C22 | semidirect |
| 16. C2×C8×D283 | C22 | semidirect |
| 18. #22583590 | C22 | semidirect |
| 23. C4×Dic566 | C22 | semidirect |
| 27. C4⋊C4×D283 | C22 | semidirect |
| 28. #22583542 | C22 | semidirect |
| 29. #22583541 | C22 | semidirect |
| 30. C4⋊(C283⋊C8) | C22 | semidirect |
| 31. #22583535 | C22 | semidirect |
| 33. #22583531 | C22 | semidirect |
| 35. (C2×D283)⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C283 | C22 | semidirect |
| 38. #102×C283 | C22 | semidirect |
| 39. #102×C283 | C22 | semidirect |
| 40. C4×C8×C283 | C22 | semidirect |
| 85. D1132 | SD16 | semidirect |
| 136. C283 | #3295 | semidirect |
| 140. #486 | D283 | semidirect |
| 154. C4⋊Q8 | C2×D283 | semidirect |
| 174. #102 | C2×D283 | semidirect |
| 175. #102 | C2×D283 | semidirect |
| 177. C4×C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827176 | 2 |
| #31827100 | 2 |
| #31826782 | 2 |
| #31826752 | 2 |
| #31826693 | 2 |
| #31826662 | 2 |
| #31826617 | 2 |
| C4×#17985381 | 2 |
| C8×D1132 | 2 |
| #102×D283 | 2 |
| #486×C283 | 2 |
| #3295 | 283 |