Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
322 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 322 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 |
|---|---|---|
| 84. C8×C83 | #108 | semidirect |
| 112. C83 | #8828 | semidirect |
| 193. C8 | #14581727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24907634 | 2 |
| #24907600 | 2 |
| #24906222 | 2 |
| #24906221 | 2 |
| #24906218 | 2 |
| C2×#19127422 | 2 |
| C83×#1566 | 2 |
| #8828 | 83 |