Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 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. #24910771 | C2 | semidirect |
| 5. #24905364 | C2 | semidirect |
| 6. #24905291 | C2 | semidirect |
| 7. C83×#1303 | C2 | semidirect |
| 194. #1303 | D83 | semidirect |
| 196. C83 | #10372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24910771 | 2 |
| #24908294 | 2 |
| #24905959 | 2 |
| #24905957 | 2 |
| #24905364 | 2 |
| #24905291 | 2 |
| C83×#1303 | 2 |
| #10372 | 83 |