Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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. #19136851 | C2 | semidirect |
| 2. #19136847 | C2 | semidirect |
| 4. #19134202 | C2 | semidirect |
| 5. #19134200 | C2 | semidirect |
| 6. C16×C43⋊C8 | C2 | semidirect |
| 7. C43×#2248 | C2 | semidirect |
| 96. #2248 | D43 | semidirect |
| 119. C43 | #12518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136851 | 2 |
| #19136847 | 2 |
| #19136844 | 2 |
| #19134202 | 2 |
| #19134200 | 2 |
| C16×C43⋊C8 | 2 |
| C43×#2248 | 2 |
| #12518 | 43 |