Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
462 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 111 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. #346×D43 | C2 | semidirect |
| 3. #334×D43 | C2 | semidirect |
| 4. #19132563 | C2 | semidirect |
| 5. #19132562 | C2 | semidirect |
| 6. #19132561 | C2 | semidirect |
| 7. C43×#1333 | C2 | semidirect |
| 20. #14582675 | C22 | semidirect |
| 22. #14582650 | C22 | semidirect |
| 25. C43×#346 | C22 | semidirect |
| 26. C43×#334 | C22 | semidirect |
| 32. D8×D43 | C8 | semidirect |
| 79. D8×C43 | C2×C8 | semidirect |
| 99. D344 | C2×C8 | semidirect |
| 168. #1333 | D43 | direct (N × H) |
| 174. D43 | #1333 | direct (N × H) |
| 190. #346 | C2×D43 | semidirect |
| 193. #334 | C2×D43 | semidirect |
| 194. C43 | C2×#1333 | semidirect |
| 250. D8 | C8×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D43 | 2 |
| #346×D43 | 2 |
| #334×D43 | 2 |
| #19132563 | 2 |
| #19132562 | 2 |
| #19132561 | 2 |
| C43×#1333 | 2 |
| C2×#1333 | 43 |