Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
474 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 73. M16×C43 | Q16 | semidirect |
| 164. C43 | #9798 | semidirect |
| 215. M16 | #10621885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583278 | 2 |
| #19135584 | 2 |
| #19133353 | 2 |
| #19133277 | 2 |
| #19133276 | 2 |
| M16×C43⋊C8 | 2 |
| C43×#1997 | 2 |
| #9798 | 43 |