Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 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 |
|---|---|---|
| 16. #19127423 | C4 | semidirect |
| 17. C8×C83⋊C8 | C4 | semidirect |
| 130. C83 | #8791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24907600 | 2 |
| #24907593 | 2 |
| #24905747 | 2 |
| #24905323 | 2 |
| #24905322 | 2 |
| #24905321 | 2 |
| C83×#1286 | 2 |
| #8791 | 83 |