Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
274 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 10. #14582729 | C4 | semidirect |
| 113. C43 | #13171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582729 | 2 |
| #19136191 | 2 |
| #19135378 | 2 |
| #19132703 | 2 |
| C2×C43×#366 | 2 |
| #13171 | 43 |