Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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×#22583618 | C2 | semidirect |
| 2. C22×#17985375 | C2 | semidirect |
| 4. #31826542 | C2 | semidirect |
| 5. #31826535 | C2 | semidirect |
| 6. #31826431 | C2 | semidirect |
| 7. #31826428 | C2 | semidirect |
| 8. #31826421 | C2 | semidirect |
| 9. #424×C283 | C2 | semidirect |
| 17. C2×#17985375 | C22 | semidirect |
| 19. C2×C8×D283 | C22 | semidirect |
| 26. (C2×D283)⋊C8 | C22 | semidirect |
| 27. #22583521 | C22 | semidirect |
| 28. C4×C283⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C283 | C22 | semidirect |
| 50. C2×C283⋊C8 | D4 | semidirect |
| 113. C283 | #2930 | semidirect |
| 120. #424 | D283 | semidirect |
| 142. C4⋊C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583618 | 2 |
| C22×#17985375 | 2 |
| #31826977 | 2 |
| #31826542 | 2 |
| #31826535 | 2 |
| #31826431 | 2 |
| #31826428 | 2 |
| #31826421 | 2 |
| #424×C283 | 2 |
| #2930 | 283 |