Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. C2×#14583315 | C2 | semidirect |
| 2. #19144239 | C2 | semidirect |
| 3. #19136695 | C2 | semidirect |
| 4. #19136678 | C2 | semidirect |
| 5. #19136379 | C2 | semidirect |
| 6. #19136311 | C2 | semidirect |
| 7. C22×D16×C43 | C2 | semidirect |
| 12. C2×#13063264 | C22 | semidirect |
| 13. C2×C16×D43 | C22 | semidirect |
| 15. #14583132 | C22 | semidirect |
| 18. #14582727 | C22 | semidirect |
| 19. #14582725 | C22 | semidirect |
| 20. #14582700 | C22 | semidirect |
| 52. C2×C16×C43 | D4 | semidirect |
| 125. C22×D16 | D43 | semidirect |
| 155. C43 | #33607 | semidirect |
| 179. C2×C16 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583315 | 2 |
| #19144239 | 2 |
| #19136695 | 2 |
| #19136678 | 2 |
| #19136379 | 2 |
| #19136311 | 2 |
| C22×D16×C43 | 2 |
| #33607 | 43 |