Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #24905569 | C2 | semidirect |
| 5. #24905568 | C2 | semidirect |
| 6. #24905564 | C2 | semidirect |
| 7. C83×#1384 | C2 | semidirect |
| 14. #19127736 | C4 | semidirect |
| 16. #106×D83 | C4 | semidirect |
| 157. #1384 | D83 | semidirect |
| 158. C83 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916055 | 2 |
| #24909083 | 2 |
| #24907506 | 2 |
| #24905569 | 2 |
| #24905568 | 2 |
| #24905564 | 2 |
| C83×#1384 | 2 |
| #12873 | 83 |