Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
732 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 243 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 |
|---|---|---|
| 3. #19135150 | C2 | semidirect |
| 4. #19134466 | C2 | semidirect |
| 6. C42×C43⋊C8 | C2 | semidirect |
| 7. C43×#1839 | C2 | semidirect |
| 65. C42×C43 | M16 | semidirect |
| 101. C43⋊C8 | #126 | semidirect |
| 119. #1839 | D43 | semidirect |
| 144. C43 | #21666 | semidirect |
| 196. 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 |
| #19135199 | 2 |
| #19135150 | 2 |
| #19134466 | 2 |
| #19134375 | 2 |
| C42×C43⋊C8 | 2 |
| C43×#1839 | 2 |
| #21666 | 43 |