Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
508 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 111 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. #19134312 | C2 | semidirect |
| 3. #19132605 | C2 | semidirect |
| 4. C43×#2112 | C2 | semidirect |
| 5. C22×D344 | C4 | semidirect |
| 10. #14583135 | C4 | semidirect |
| 12. C2×#13063259 | C4 | semidirect |
| 15. #14582662 | C22 | semidirect |
| 19. C43×C22⋊C16 | C22 | semidirect |
| 151. #2112 | D43 | semidirect |
| 173. C22⋊C16 | C2×D43 | semidirect |
| 176. C43 | #11705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583135 | 2 |
| #19134312 | 2 |
| #19132605 | 2 |
| C43×#2112 | 2 |
| #11705 | 43 |