Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
786 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 109 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. #19134530 | C2 | semidirect |
| 5. #19133167 | C2 | semidirect |
| 6. #19132443 | C2 | semidirect |
| 7. C43×#2434 | C2 | semidirect |
| 129. C22⋊C4×C43 | SD16 | semidirect |
| 226. #2434 | D43 | semidirect |
| 262. C43 | #9949 | semidirect |
| 373. C22⋊C4 | #10621884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145348 | 2 |
| C2×#14583038 | 2 |
| #19135431 | 2 |
| #19134530 | 2 |
| #19133167 | 2 |
| #19132443 | 2 |
| C43×#2434 | 2 |
| #9949 | 43 |