Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
294 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 294 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 |
|---|---|---|
| 17. #14582719 | C4 | semidirect |
| 136. C43 | #13187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582722 | 2 |
| C2×#14582721 | 2 |
| C2×#14582719 | 2 |
| #19134756 | 2 |
| #19134476 | 2 |
| #19132700 | 2 |
| C43×#1386 | 2 |
| #13187 | 43 |