Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
676 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×#14583328 | C2 | semidirect |
| 2. #19146316 | C2 | semidirect |
| 3. #19136848 | C2 | semidirect |
| 4. #19136687 | C2 | semidirect |
| 5. #19136640 | C2 | semidirect |
| 6. #19136536 | C2 | semidirect |
| 7. C16×D172 | C2 | semidirect |
| 8. C4×D16×C43 | C2 | semidirect |
| 52. D16×C43 | D4 | semidirect |
| 122. C4×C43 | #508 | semidirect |
| 133. C4×D16 | D43 | semidirect |
| 160. C43 | #33849 | semidirect |
| 179. D16 | D172 | semidirect |
| 255. C4 | #14583328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583328 | 2 |
| #19146316 | 2 |
| #19136848 | 2 |
| #19136687 | 2 |
| #19136640 | 2 |
| #19136536 | 2 |
| C16×D172 | 2 |
| C4×D16×C43 | 2 |
| #33849 | 43 |