Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24917995 | C2 | semidirect |
| 5. #24905568 | C2 | semidirect |
| 6. #24905550 | C2 | semidirect |
| 7. C83×#1384 | C2 | semidirect |
| 30. C2×Dic332 | Q8 | semidirect |
| 32. C2×D664 | Q8 | semidirect |
| 162. #1384 | D83 | semidirect |
| 164. C83 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917995 | 2 |
| #24909198 | 2 |
| C2×#19127512 | 2 |
| #24908359 | 2 |
| #24905568 | 2 |
| #24905550 | 2 |
| C83×#1384 | 2 |
| #13374 | 83 |