Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 15. #19127518 | C4 | semidirect |
| 136. C83 | #13139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127518 | 2 |
| C2×#19127516 | 2 |
| #24908332 | 2 |
| #24907371 | 2 |
| #24905561 | 2 |
| #24905546 | 2 |
| C2×#365×C83 | 2 |
| #13139 | 83 |