Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 91 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. #19136868 | C2 | semidirect |
| 3. #19136820 | C2 | semidirect |
| 4. #19136818 | C2 | semidirect |
| 5. #19134187 | C2 | semidirect |
| 6. C8×C43⋊C16 | C2 | semidirect |
| 7. C43×#1706 | C2 | semidirect |
| 69. C43⋊C16 | SD16 | semidirect |
| 88. C8×C43 | D16 | semidirect |
| 110. #1706 | D43 | semidirect |
| 132. C43 | #12503 | semidirect |
| 198. C8 | #13063266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136868 | 2 |
| #19136844 | 2 |
| #19136820 | 2 |
| #19136818 | 2 |
| #19134187 | 2 |
| C8×C43⋊C16 | 2 |
| C43×#1706 | 2 |
| #12503 | 43 |