Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
642 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 215 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. #19135317 | C2 | semidirect |
| 4. #19135162 | C2 | semidirect |
| 6. #19134747 | C2 | semidirect |
| 7. C43×#1839 | C2 | semidirect |
| 64. C42×C43 | M16 | semidirect |
| 121. #1839 | D43 | semidirect |
| 143. C43 | #23378 | semidirect |
| 194. C42 | #10621872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13063319 | 2 |
| #19135317 | 2 |
| #19135209 | 2 |
| #19135162 | 2 |
| #19134779 | 2 |
| #19134747 | 2 |
| C43×#1839 | 2 |
| #23378 | 43 |