Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
294 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 59 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. #19147731 | C2 | semidirect |
| 2. #19136910 | C2 | semidirect |
| 3. #19136698 | C2 | semidirect |
| 4. #19132783 | C2 | semidirect |
| 5. C43×#1400 | C2 | semidirect |
| 11. C2×D688 | C22 | semidirect |
| 15. #14582727 | C22 | semidirect |
| 18. C43×M64 | C22 | semidirect |
| 30. Dic344 | D4 | semidirect |
| 35. D688 | D4 | semidirect |
| 111. #1400 | D43 | semidirect |
| 127. M64 | C2×D43 | semidirect |
| 130. C43 | #13667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147731 | 2 |
| #19136910 | 2 |
| #19136698 | 2 |
| #19132783 | 2 |
| C43×#1400 | 2 |
| #13667 | 43 |