Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
402 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 157 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. #31826544 | C2 | semidirect |
| 3. #31826542 | C2 | semidirect |
| 4. #31826538 | C2 | semidirect |
| 5. #31826535 | C2 | semidirect |
| 6. #31826526 | C2 | semidirect |
| 7. #31826430 | C2 | semidirect |
| 8. #31826427 | C2 | semidirect |
| 9. #433×C283 | C2 | semidirect |
| 14. C2×#17985375 | C22 | semidirect |
| 15. C2×C8×D283 | C22 | semidirect |
| 22. C4⋊(C283⋊C8) | C22 | semidirect |
| 26. (C2×D283)⋊C8 | C22 | semidirect |
| 27. (C2×D283)⋊C8 | C22 | semidirect |
| 28. #22583521 | C22 | semidirect |
| 29. C4×C283⋊C8 | C22 | semidirect |
| 31. C4⋊C8×C283 | C22 | semidirect |
| 33. #97×C283 | C22 | semidirect |
| 34. C4×C8×C283 | C22 | semidirect |
| 114. C283 | #2978 | semidirect |
| 122. #433 | D283 | semidirect |
| 139. C4⋊C8 | C2×D283 | semidirect |
| 147. #97 | C2×D283 | semidirect |
| 149. C4×C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826977 | 2 |
| #31826544 | 2 |
| #31826542 | 2 |
| #31826538 | 2 |
| #31826535 | 2 |
| #31826526 | 2 |
| #31826430 | 2 |
| #31826427 | 2 |
| #433×C283 | 2 |
| #2978 | 283 |