Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
316 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 22. #13063265 | Q8 | semidirect |
| 120. C43 | #13270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136361 | 2 |
| #19136200 | 2 |
| #19132681 | 2 |
| #19132677 | 2 |
| C43×#2960 | 2 |
| #13270 | 43 |