Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #19132417 | C2 | semidirect |
| 171. C43 | #7708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19142947 | 2 |
| #19134663 | 2 |
| #19132417 | 2 |
| C43×#1749 | 2 |
| #7708 | 43 |