Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24918586 | C2 | semidirect |
| 3. C2×#19127907 | C2 | semidirect |
| 4. #24906136 | C2 | semidirect |
| 5. #24905861 | C2 | semidirect |
| 6. #24905783 | C2 | semidirect |
| 7. C83×#1301 | C2 | semidirect |
| 224. #1301 | D83 | semidirect |
| 225. C83 | #10184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918586 | 2 |
| #24916929 | 2 |
| C2×#19127907 | 2 |
| #24906136 | 2 |
| #24905861 | 2 |
| #24905783 | 2 |
| C83×#1301 | 2 |
| #10184 | 83 |