Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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. #19136878 | C2 | semidirect |
| 3. #19134110 | C2 | semidirect |
| 4. #19132646 | C2 | semidirect |
| 5. #19132576 | C2 | semidirect |
| 68. D8×C43 | Q16 | semidirect |
| 162. C43 | #12414 | semidirect |
| 205. D8 | #10621885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147551 | 2 |
| #19136878 | 2 |
| #19134110 | 2 |
| #19132646 | 2 |
| #19132576 | 2 |
| #19132562 | 2 |
| C43×#2226 | 2 |
| #12414 | 43 |