Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
552 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 2. #24918413 | C2 | semidirect |
| 4. #24908451 | C2 | semidirect |
| 5. #24906057 | C2 | semidirect |
| 7. C83×#1299 | C2 | semidirect |
| 187. #1299 | D83 | semidirect |
| 188. C83 | #10107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918851 | 2 |
| #24918413 | 2 |
| #24917922 | 2 |
| #24908451 | 2 |
| #24906057 | 2 |
| #24905879 | 2 |
| C83×#1299 | 2 |
| #10107 | 83 |