Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 2. #24909228 | C2 | semidirect |
| 5. #24907586 | C2 | semidirect |
| 6. #24905579 | C2 | semidirect |
| 7. C83×#1384 | C2 | semidirect |
| 11. #19127812 | C4 | semidirect |
| 144. #1384 | D83 | semidirect |
| 145. C83 | #12826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916314 | 2 |
| #24909228 | 2 |
| C2×#19127515 | 2 |
| #24909178 | 2 |
| #24907586 | 2 |
| #24905579 | 2 |
| C83×#1384 | 2 |
| #12826 | 83 |