Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
254 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 14. #19127524 | C4 | semidirect |
| 116. C83 | #13117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909236 | 2 |
| #24908211 | 2 |
| C4×#14581728 | 2 |
| #24905578 | 2 |
| #24905575 | 2 |
| #24905567 | 2 |
| C83×#1376 | 2 |
| #13117 | 83 |