Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
304 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 87 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. #24906254 | C2 | semidirect |
| 5. #24905756 | C2 | semidirect |
| 6. #24905301 | C2 | semidirect |
| 7. C83×#1299 | C2 | semidirect |
| 154. #1299 | D83 | semidirect |
| 156. C83 | #9588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24906254 | 2 |
| #24906123 | 2 |
| #24905913 | 2 |
| #24905881 | 2 |
| #24905756 | 2 |
| #24905301 | 2 |
| C83×#1299 | 2 |
| #9588 | 83 |