Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
306 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 12. #19128103 | C4 | semidirect |
| 13. #19128099 | C4 | semidirect |
| 33. #14581732 | Q8 | semidirect |
| 35. C2×C83⋊C16 | Q8 | semidirect |
| 131. C83 | #13291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917994 | 2 |
| #24909068 | 2 |
| #24905577 | 2 |
| #24905568 | 2 |
| #24905564 | 2 |
| #24905563 | 2 |
| C83×#1833 | 2 |
| #13291 | 83 |