Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
402 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 109. C42×C83 | Q16 | semidirect |
| 181. C83 | #10522 | semidirect |
| 283. C42 | #13050580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918805 | 2 |
| #24908440 | 2 |
| #24907615 | 2 |
| #24906154 | 2 |
| #24906153 | 2 |
| #24905337 | 2 |
| C83×#1994 | 2 |
| #10522 | 83 |