Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
346 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 13. #19127521 | C4 | semidirect |
| 104. C83 | #12659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127521 | 2 |
| C2×#19127479 | 2 |
| #97×Dic83 | 2 |
| #24905546 | 2 |
| C2×#347×C83 | 2 |
| #12659 | 83 |