Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1236 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 231 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. #19143075 | C2 | semidirect |
| 3. #19135144 | C2 | semidirect |
| 4. #19135010 | C2 | semidirect |
| 5. #19134707 | C2 | semidirect |
| 6. #19134519 | C2 | semidirect |
| 7. C43×#1784 | C2 | semidirect |
| 189. #1784 | D43 | semidirect |
| 217. C43 | #21780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19148246 | 2 |
| #19143075 | 2 |
| #19135144 | 2 |
| #19135010 | 2 |
| #19134707 | 2 |
| #19134519 | 2 |
| C43×#1784 | 2 |
| #21780 | 43 |