Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
440 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 73 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. #24909135 | C2 | semidirect |
| 2. #24909113 | C2 | semidirect |
| 3. #24908011 | C2 | semidirect |
| 4. #24907991 | C2 | semidirect |
| 5. #24907748 | C2 | semidirect |
| 6. #24905592 | C2 | semidirect |
| 209. C83 | #13432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909135 | 2 |
| #24909113 | 2 |
| #24908011 | 2 |
| #24907991 | 2 |
| #24907748 | 2 |
| #24905592 | 2 |
| C83×#3199 | 2 |
| #13432 | 83 |