Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
342 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 12. #19127728 | C4 | semidirect |
| 13. #19127728 | C4 | semidirect |
| 18. C4×#13050574 | C4 | semidirect |
| 19. C2×C4×C83⋊C8 | C4 | semidirect |
| 174. C83 | #12864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916107 | 2 |
| #24907567 | 2 |
| #24905593 | 2 |
| #24905591 | 2 |
| #24905585 | 2 |
| #24905583 | 2 |
| C83×#1827 | 2 |
| #12864 | 83 |