Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
456 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 456 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. #31826360 | C2 | semidirect |
| 4. #31826346 | C2 | semidirect |
| 6. #31826333 | C2 | semidirect |
| 7. #384×C283 | C2 | semidirect |
| 9. #22583604 | C4 | semidirect |
| 28. Dic283⋊C4 | C2×C4 | semidirect |
| 37. C42×C283 | C2×C4 | semidirect |
| 72. C283 | #2383 | semidirect |
| 79. #384 | D283 | semidirect |
| 110. C42 | C4×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583604 | 2 |
| #31826360 | 2 |
| #31826355 | 2 |
| #31826346 | 2 |
| #31826336 | 2 |
| #31826333 | 2 |
| #384×C283 | 2 |
| #2383 | 283 |