Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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. C22×C16×D43 | C2 | semidirect |
| 3. C2×#14582707 | C2 | semidirect |
| 4. C2×#14582705 | C2 | semidirect |
| 5. #19134630 | C2 | semidirect |
| 6. #19132690 | C2 | semidirect |
| 7. C43×#1382 | C2 | semidirect |
| 51. C2×C43⋊C16 | D4 | semidirect |
| 63. C2×C16×C43 | D4 | semidirect |
| 167. C2×D43 | #359 | semidirect |
| 181. #1382 | D43 | semidirect |
| 207. C43 | #13063 | semidirect |
| 239. C2×C16 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D43 | 2 |
| #19144177 | 2 |
| C2×#14582707 | 2 |
| C2×#14582705 | 2 |
| #19134630 | 2 |
| #19132690 | 2 |
| C43×#1382 | 2 |
| #13063 | 43 |