Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
486 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. C2×#14582676 | C2 | semidirect |
| 5. #19134482 | C2 | semidirect |
| 6. #19132702 | C2 | semidirect |
| 7. C43×#1383 | C2 | semidirect |
| 12. #14583010 | C4 | semidirect |
| 17. #14582711 | C4 | semidirect |
| 18. #14582701 | C4 | semidirect |
| 39. #13063265 | C2×C4 | semidirect |
| 41. #13063259 | C2×C4 | semidirect |
| 53. C2×C16×C43 | C2×C4 | semidirect |
| 55. #108×C43 | C2×C4 | semidirect |
| 147. #1383 | D43 | semidirect |
| 169. C43 | #12647 | semidirect |
| 192. C2×C16 | C4×D43 | semidirect |
| 194. #108 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583010 | 2 |
| C2×#14582711 | 2 |
| #19136312 | 2 |
| C2×#14582676 | 2 |
| #19134482 | 2 |
| #19132702 | 2 |
| C43×#1383 | 2 |
| #12647 | 43 |