Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
500 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 7. #19127500 | C4 | direct (N × H) |
| 129. C4×C83 | #356 | semidirect |
| 140. C83 | C4×#356 | semidirect |
| 265. C4 | #19127500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127500 | 2 |
| C4×#14581711 | 2 |
| #24905590 | 2 |
| C4×C4⋊Q8×C83 | 2 |
| C4×#356 | 83 |