Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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. C4×#13063264 | C2 | semidirect |
| 3. #19133342 | C2 | semidirect |
| 4. #19132557 | C2 | semidirect |
| 5. #19132556 | C2 | semidirect |
| 6. #19132555 | C2 | semidirect |
| 7. C43×#1331 | C2 | semidirect |
| 21. C4×C43⋊C16 | C22 | semidirect |
| 22. #14582652 | C22 | semidirect |
| 25. C4×C16×C43 | C22 | semidirect |
| 26. C43×#335 | C22 | semidirect |
| 32. D8×D43 | C8 | semidirect |
| 172. #1331 | D43 | semidirect |
| 194. C4×C16 | C2×D43 | semidirect |
| 196. #335 | C2×D43 | semidirect |
| 198. C43 | #11593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D43 | 2 |
| C4×#13063264 | 2 |
| #19133342 | 2 |
| #19132557 | 2 |
| #19132556 | 2 |
| #19132555 | 2 |
| C43×#1331 | 2 |
| #11593 | 43 |