Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
690 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 105 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. #24918388 | C2 | semidirect |
| 3. #24908291 | C2 | semidirect |
| 4. #24906144 | C2 | semidirect |
| 5. #24906131 | C2 | semidirect |
| 6. #24905296 | C2 | semidirect |
| 7. C83×#2858 | C2 | semidirect |
| 192. #2858 | D83 | semidirect |
| 197. C83 | #10281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918388 | 2 |
| #24918381 | 2 |
| #24908291 | 2 |
| #24906144 | 2 |
| #24906131 | 2 |
| #24905296 | 2 |
| C83×#2858 | 2 |
| #10281 | 83 |