Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
392 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 175. C83 | #9727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918045 | 2 |
| C4×#14581727 | 2 |
| #24906058 | 2 |
| #24906057 | 2 |
| #24905883 | 2 |
| #24905753 | 2 |
| C83×#1485 | 2 |
| #9727 | 83 |