Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24909218 | C2 | semidirect |
| 5. #24907624 | C2 | semidirect |
| 6. #24905568 | C2 | semidirect |
| 7. C83×#1386 | C2 | semidirect |
| 11. #19127795 | C4 | semidirect |
| 13. #19127783 | C4 | semidirect |
| 164. #1386 | D83 | semidirect |
| 165. C83 | #12817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916234 | 2 |
| #24909218 | 2 |
| C2×#19127512 | 2 |
| C2×#19127510 | 2 |
| #24907624 | 2 |
| #24905568 | 2 |
| C83×#1386 | 2 |
| #12817 | 83 |