Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
324 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 103 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. #19127516 | C4 | semidirect |
| 149. C83 | #13135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909252 | 2 |
| C2×#19127516 | 2 |
| #24909182 | 2 |
| #24908324 | 2 |
| #24905573 | 2 |
| #24905545 | 2 |
| C83×#1772 | 2 |
| #13135 | 83 |