Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
500 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 123 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. #24912705 | C2 | semidirect |
| 3. #24905346 | C2 | semidirect |
| 4. #24905303 | C2 | semidirect |
| 138. C83 | #10351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24912705 | 2 |
| #24908391 | 2 |
| #24905346 | 2 |
| #24905303 | 2 |
| C83×#1957 | 2 |
| #10351 | 83 |