Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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×#17985379 | C2 | semidirect |
| 2. C2×#22583618 | C2 | semidirect |
| 3. #31827039 | C2 | semidirect |
| 5. #31826714 | C2 | semidirect |
| 6. #31826697 | C2 | semidirect |
| 7. #31826501 | C2 | semidirect |
| 8. #31826471 | C2 | semidirect |
| 9. #419×C283 | C2 | semidirect |
| 16. C2×#17985375 | C22 | semidirect |
| 18. C2×C8×D283 | C22 | semidirect |
| 24. #22583586 | C22 | semidirect |
| 28. #22583543 | C22 | semidirect |
| 29. #22583541 | C22 | semidirect |
| 34. #103×C283 | C22 | semidirect |
| 50. C2×C283⋊C8 | D4 | semidirect |
| 120. C283 | #3057 | semidirect |
| 129. #419 | D283 | semidirect |
| 154. #103 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985379 | 2 |
| C2×#22583618 | 2 |
| #31827039 | 2 |
| #31827034 | 2 |
| #31826714 | 2 |
| #31826697 | 2 |
| #31826501 | 2 |
| #31826471 | 2 |
| #419×C283 | 2 |
| #3057 | 283 |