Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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. #19147732 | C2 | semidirect |
| 2. #19136908 | C2 | semidirect |
| 3. #19136712 | C2 | semidirect |
| 4. #19132785 | C2 | semidirect |
| 5. #19132780 | C2 | semidirect |
| 6. #19132736 | C2 | semidirect |
| 7. C2×C43×D32 | C2 | semidirect |
| 18. #14582733 | C22 | semidirect |
| 19. #14582729 | C22 | semidirect |
| 22. C2×D16×C43 | C22 | semidirect |
| 24. C2×C32×C43 | C22 | semidirect |
| 118. C2×D32 | D43 | semidirect |
| 136. C2×D16 | C2×D43 | semidirect |
| 143. C2×C32 | C2×D43 | semidirect |
| 146. C43 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147732 | 2 |
| #19136908 | 2 |
| #19136712 | 2 |
| #19132785 | 2 |
| #19132780 | 2 |
| #19132736 | 2 |
| C2×C43×D32 | 2 |
| #13669 | 43 |