Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #24906058 | C2 | semidirect |
| 5. #24905352 | C2 | semidirect |
| 6. #24905300 | C2 | semidirect |
| 7. C83×#1493 | C2 | semidirect |
| 195. #1493 | D83 | semidirect |
| 199. C83 | #9214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917528 | 2 |
| #24916105 | 2 |
| #24906058 | 2 |
| #24905900 | 2 |
| #24905352 | 2 |
| #24905300 | 2 |
| C83×#1493 | 2 |
| #9214 | 83 |