Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1170 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 147 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. #19134357 | C2 | semidirect |
| 3. C2×#14582638 | C2 | semidirect |
| 4. C43×#1749 | C2 | semidirect |
| 15. C2×#13063236 | C22 | semidirect |
| 20. C2×#97×C43 | C22 | semidirect |
| 180. C22×C43 | #329 | semidirect |
| 205. #1749 | D43 | semidirect |
| 229. C2×#97 | C2×D43 | semidirect |
| 233. C43 | #8334 | semidirect |
| 399. C22 | #14582638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13063313 | 2 |
| #19134357 | 2 |
| C2×#14582638 | 2 |
| C43×#1749 | 2 |
| #8334 | 43 |