Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
602 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 127 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. #19143636 | C2 | semidirect |
| 2. #19132986 | C2 | semidirect |
| 3. #19132916 | C2 | semidirect |
| 4. #19132424 | C2 | semidirect |
| 28. C4×C43⋊C8 | D4 | semidirect |
| 64. C2×D4×C43 | M16 | semidirect |
| 86. C42×C43 | M16 | semidirect |
| 184. C43 | #9105 | semidirect |
| 228. C2×D4 | #10621877 | semidirect |
| 253. C42 | #10621877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143636 | 2 |
| #19132986 | 2 |
| #19132916 | 2 |
| #19132424 | 2 |
| C43×#2328 | 2 |
| #9105 | 43 |