Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 542 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. #19137780 | C2 | semidirect |
| 5. C2×#14582640 | C2 | semidirect |
| 6. #19132477 | C2 | semidirect |
| 7. C43×#1295 | C2 | semidirect |
| 11. #14583264 | C4 | semidirect |
| 216. #1295 | D43 | semidirect |
| 247. C43 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583264 | 2 |
| #19137780 | 2 |
| #19135419 | 2 |
| #19135418 | 2 |
| C2×#14582640 | 2 |
| #19132477 | 2 |
| C43×#1295 | 2 |
| #9002 | 43 |