Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 105. M16×C83 | Q16 | semidirect |
| 187. C83 | #10203 | semidirect |
| 271. M16 | #13050580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918805 | 2 |
| #24918614 | 2 |
| #24908407 | 2 |
| #24908387 | 2 |
| #24905962 | 2 |
| #24905314 | 2 |
| C83×#3165 | 2 |
| #10203 | 83 |