Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24918850 | C2 | semidirect |
| 2. #24918657 | C2 | semidirect |
| 3. #24908296 | C2 | semidirect |
| 4. #24905976 | C2 | semidirect |
| 5. #24905971 | C2 | semidirect |
| 6. #24905373 | C2 | semidirect |
| 210. C83 | #10214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918850 | 2 |
| #24918657 | 2 |
| #24908296 | 2 |
| #24905976 | 2 |
| #24905971 | 2 |
| #24905373 | 2 |
| C83×#3214 | 2 |
| #10214 | 83 |