Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
552 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 2. #24918408 | C2 | semidirect |
| 4. #24908452 | C2 | semidirect |
| 6. #24905353 | C2 | semidirect |
| 7. C83×#1526 | C2 | semidirect |
| 185. #1526 | 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 |
|---|---|
| #24918846 | 2 |
| #24918408 | 2 |
| #24917922 | 2 |
| #24908452 | 2 |
| #24905881 | 2 |
| #24905353 | 2 |
| C83×#1526 | 2 |
| #10107 | 83 |