Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
552 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 95. M16×C83 | Q16 | semidirect |
| 167. C83 | #10155 | semidirect |
| 247. M16 | #13050580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918408 | 2 |
| C2×#19128080 | 2 |
| #24908452 | 2 |
| #24906148 | 2 |
| #24905918 | 2 |
| #24905301 | 2 |
| C83×#3165 | 2 |
| #10155 | 83 |