Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1206 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 403 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. #19136957 | C2 | semidirect |
| 3. C4×#13063258 | C2 | semidirect |
| 4. #19134423 | C2 | semidirect |
| 5. #19134420 | C2 | semidirect |
| 6. #19134282 | C2 | semidirect |
| 7. C43×#2275 | C2 | semidirect |
| 10. C4×#10621882 | C4 | semidirect |
| 31. C4×D172 | C2×C4 | semidirect |
| 35. #13063258 | C2×C4 | semidirect |
| 36. #13063246 | C2×C4 | semidirect |
| 37. #13063245 | C2×C4 | semidirect |
| 39. C4×C43⋊C8 | C2×C4 | semidirect |
| 44. C4×D4×C43 | C2×C4 | semidirect |
| 73. #10621882 | C42 | semidirect |
| 125. #2275 | D43 | semidirect |
| 152. C43 | #20508 | semidirect |
| 163. C4×D4 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#10621882 | 2 |
| #19136957 | 2 |
| C4×#13063258 | 2 |
| #19134423 | 2 |
| #19134420 | 2 |
| #19134282 | 2 |
| C43×#2275 | 2 |
| #20508 | 43 |