Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
698 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 129 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. C22×D688 | C2 | semidirect |
| 2. C2×#14583276 | C2 | semidirect |
| 3. C2×#14582701 | C2 | semidirect |
| 4. #19135461 | C2 | semidirect |
| 5. C43×#1374 | C2 | semidirect |
| 35. C2×D344 | D4 | semidirect |
| 48. C2×C16×C43 | D4 | semidirect |
| 103. C2×C4×C43 | D16 | semidirect |
| 150. #1374 | D43 | semidirect |
| 172. C43 | #13325 | semidirect |
| 199. C2×C16 | D172 | semidirect |
| 267. C2×C4 | D688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D688 | 2 |
| C2×#14583276 | 2 |
| C2×#14582701 | 2 |
| #19135461 | 2 |
| C43×#1374 | 2 |
| #13325 | 43 |