Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 17. #19127517 | 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×#19127517 | 2 |
| #24908325 | 2 |
| #24907344 | 2 |
| #24905572 | 2 |
| #24905544 | 2 |
| C83×#2141 | 2 |
| #13135 | 83 |