Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
498 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 105 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. #19143448 | C2 | semidirect |
| 3. #19136331 | C2 | semidirect |
| 4. #19136310 | C2 | semidirect |
| 5. #19132696 | C2 | semidirect |
| 6. #19132681 | C2 | semidirect |
| 7. C43×#1976 | C2 | semidirect |
| 12. C2×#13063268 | C4 | semidirect |
| 13. C2×#13063266 | C4 | semidirect |
| 45. C2×C43⋊C16 | C2×C4 | semidirect |
| 54. C2×Q16×C43 | C2×C4 | semidirect |
| 56. C2×D8×C43 | C2×C4 | semidirect |
| 172. #1976 | D43 | semidirect |
| 200. C43 | #13033 | semidirect |
| 207. C2×Q16 | C4×D43 | semidirect |
| 215. C2×D8 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583334 | 2 |
| #19143448 | 2 |
| #19136331 | 2 |
| #19136310 | 2 |
| #19132696 | 2 |
| #19132681 | 2 |
| C43×#1976 | 2 |
| #13033 | 43 |