Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
270 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 14. #19127524 | C4 | semidirect |
| 126. C83 | #13114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127524 | 2 |
| #24908204 | 2 |
| #24907371 | 2 |
| #24905571 | 2 |
| #24905563 | 2 |
| #24905546 | 2 |
| C83×#1387 | 2 |
| #13114 | 83 |