Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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. #31826369 | C2 | semidirect |
| 3. #31826357 | C2 | semidirect |
| 4. #31826355 | C2 | semidirect |
| 6. #31826339 | C2 | semidirect |
| 7. #31826336 | C2 | semidirect |
| 8. #31826331 | C2 | semidirect |
| 9. #382×C283 | C2 | semidirect |
| 13. #22583598 | C4 | semidirect |
| 35. C2×Dic566 | C2×C4 | semidirect |
| 51. (C2×D283)⋊C4 | C2×C4 | semidirect |
| 52. (C2×D283)⋊C4 | C2×C4 | semidirect |
| 61. C42×C283 | C2×C4 | semidirect |
| 127. C283 | #2379 | semidirect |
| 137. #382 | D283 | semidirect |
| 189. C42 | C4×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583598 | 2 |
| #31826369 | 2 |
| #31826357 | 2 |
| #31826355 | 2 |
| #31826343 | 2 |
| #31826339 | 2 |
| #31826336 | 2 |
| #31826331 | 2 |
| #382×C283 | 2 |
| #2379 | 283 |