Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
680 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19134583 | C2 | semidirect |
| 3. #19132720 | C2 | semidirect |
| 11. C2×C4×D4×C43 | C4 | semidirect |
| 14. C43×#390 | C4 | semidirect |
| 16. C43×#384 | C4 | semidirect |
| 17. C43×C43 | C4 | semidirect |
| 59. C2×D4×C43 | C4⋊C4 | semidirect |
| 90. C42×C43 | C4⋊C4 | semidirect |
| 165. C4×C43 | #353 | semidirect |
| 181. C2×C4×D4 | Dic43 | semidirect |
| 185. #390 | Dic43 | semidirect |
| 187. #384 | Dic43 | semidirect |
| 189. C43 | Dic43 | semidirect |
| 192. C43 | #12797 | semidirect |
| 234. C2×D4 | C4⋊Dic43 | semidirect |
| 268. C42 | C4⋊Dic43 | semidirect |
| 340. C4 | #14582692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582692 | 2 |
| #19134583 | 2 |
| #19132720 | 2 |
| C4×#127×C43 | 2 |
| #12797 | 43 |