Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
276 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#19127523 | C2 | semidirect |
| 4. #24905577 | C2 | semidirect |
| 5. #24905570 | C2 | semidirect |
| 6. #24905566 | C2 | semidirect |
| 140. C83 | #13502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127523 | 2 |
| #24909084 | 2 |
| #24907517 | 2 |
| #24905577 | 2 |
| #24905570 | 2 |
| #24905566 | 2 |
| C83×#1815 | 2 |
| #13502 | 83 |