Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #24906135 | C2 | semidirect |
| 5. #24905858 | C2 | semidirect |
| 6. #24905366 | C2 | semidirect |
| 7. C83×#2546 | C2 | semidirect |
| 214. #2546 | D83 | semidirect |
| 219. C83 | #10243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918584 | 2 |
| #24916935 | 2 |
| #24906135 | 2 |
| #24905957 | 2 |
| #24905858 | 2 |
| #24905366 | 2 |
| C83×#2546 | 2 |
| #10243 | 83 |