Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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. #24907501 | C2 | semidirect |
| 4. #24905369 | C2 | semidirect |
| 5. C83×#1807 | C2 | semidirect |
| 6. C2×#14581798 | C4 | semidirect |
| 13. #19127727 | C4 | semidirect |
| 14. #19127667 | C4 | semidirect |
| 17. #19127656 | C4 | semidirect |
| 187. #1807 | D83 | semidirect |
| 190. C83 | #8629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916157 | 2 |
| #24907501 | 2 |
| #24906004 | 2 |
| #24905369 | 2 |
| C83×#1807 | 2 |
| #8629 | 83 |