Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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. #19136504 | C2 | semidirect |
| 4. #19132658 | C2 | semidirect |
| 6. C16×C43⋊C8 | C2 | semidirect |
| 7. C43×Q8⋊C16 | C2 | semidirect |
| 67. C43⋊C16 | SD16 | semidirect |
| 88. C43⋊C8 | M32 | semidirect |
| 106. Q8⋊C16 | D43 | semidirect |
| 128. C43 | #12051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136504 | 2 |
| #19136426 | 2 |
| C8×#10621884 | 2 |
| #19132658 | 2 |
| #19132551 | 2 |
| C16×C43⋊C8 | 2 |
| C43×Q8⋊C16 | 2 |
| #12051 | 43 |