Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
580 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #19134875 | C2 | semidirect |
| 4. #19132713 | C2 | semidirect |
| 11. #14582692 | C4 | semidirect |
| 29. #13063240 | C2×C4 | semidirect |
| 59. C2×D4×C43 | C4⋊C4 | semidirect |
| 79. C42×C43 | C4⋊C4 | semidirect |
| 181. C43 | #12966 | semidirect |
| 221. C2×D4 | Dic43⋊C4 | semidirect |
| 251. C42 | Dic43⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582692 | 2 |
| #19134994 | 2 |
| #19134875 | 2 |
| #19132713 | 2 |
| C43×#2380 | 2 |
| #12966 | 43 |