Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 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. #31826345 | C2 | semidirect |
| 3. #31826344 | C2 | semidirect |
| 4. #31826343 | C2 | semidirect |
| 5. #31826342 | C2 | semidirect |
| 6. #31826341 | C2 | semidirect |
| 7. #31826341 | C2 | semidirect |
| 8. #31826332 | C2 | semidirect |
| 9. #386×C283 | C2 | semidirect |
| 15. #22583606 | C4 | semidirect |
| 35. C2×D1132 | C2×C4 | semidirect |
| 40. C2×C22⋊D283 | C2×C4 | semidirect |
| 41. C2×C22⋊D283 | C2×C4 | semidirect |
| 55. C4×Dic283 | C2×C4 | semidirect |
| 60. C2×D4×C283 | C2×C4 | semidirect |
| 147. C283 | #2380 | semidirect |
| 156. #386 | D283 | semidirect |
| 194. C2×D4 | C4×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583606 | 2 |
| #31826345 | 2 |
| #31826344 | 2 |
| #31826343 | 2 |
| #31826342 | 2 |
| #31826341 | 2 |
| #31826332 | 2 |
| #386×C283 | 2 |
| #2380 | 283 |