Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
874 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 2. C2×#14582714 | C2 | semidirect |
| 3. #19136322 | C2 | semidirect |
| 4. #19136216 | C2 | semidirect |
| 5. C43×#1813 | C2 | semidirect |
| 168. #1813 | D43 | semidirect |
| 191. C43 | #12744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583716 | 2 |
| C2×#14582714 | 2 |
| #19136322 | 2 |
| #19136216 | 2 |
| C43×#1813 | 2 |
| #12744 | 43 |