Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
348 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 67 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. #24909658 | C2 | semidirect |
| 2. #24909641 | C2 | semidirect |
| 3. #24908886 | C2 | semidirect |
| 4. #24905475 | C2 | semidirect |
| 5. #24905472 | C2 | semidirect |
| 6. #24905387 | C2 | semidirect |
| 176. C83 | #12280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909658 | 2 |
| #24909641 | 2 |
| #24908886 | 2 |
| #24905475 | 2 |
| #24905472 | 2 |
| #24905387 | 2 |
| C83×#3191 | 2 |
| #12280 | 83 |