Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
464 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24918679 | C2 | semidirect |
| 4. #24908443 | C2 | semidirect |
| 5. #24905976 | C2 | semidirect |
| 7. C83×#1307 | C2 | semidirect |
| 198. #1307 | D83 | semidirect |
| 199. C83 | #10215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918851 | 2 |
| #24918679 | 2 |
| #24918476 | 2 |
| #24908443 | 2 |
| #24905976 | 2 |
| #24905972 | 2 |
| C83×#1307 | 2 |
| #10215 | 83 |