Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. #19136216 | C2 | semidirect |
| 3. #19132579 | C2 | semidirect |
| 4. C43×#1812 | C2 | semidirect |
| 5. C22×D344 | C4 | semidirect |
| 8. #14583152 | C4 | semidirect |
| 12. #14582937 | C4 | semidirect |
| 15. #14582681 | C22 | semidirect |
| 19. C43×H(3,ℤ/4) | C22 | semidirect |
| 147. #1812 | D43 | semidirect |
| 169. H(3,ℤ/4) | C2×D43 | semidirect |
| 170. C43 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144243 | 2 |
| #19136216 | 2 |
| #19132579 | 2 |
| C43×#1812 | 2 |
| #11868 | 43 |