Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
516 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #19143446 | C2 | semidirect |
| 3. C2×#14582711 | C2 | semidirect |
| 4. #19136310 | C2 | semidirect |
| 5. #19135503 | C2 | semidirect |
| 6. #19132683 | C2 | semidirect |
| 7. C43×#1382 | C2 | semidirect |
| 13. C2×D688 | C4 | semidirect |
| 37. C2×D344 | C2×C4 | semidirect |
| 59. C2×C16×C43 | C2×C4 | semidirect |
| 165. #1382 | D43 | semidirect |
| 191. C43 | #13017 | semidirect |
| 220. C2×C16 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D688 | 2 |
| #19143446 | 2 |
| C2×#14582711 | 2 |
| #19136310 | 2 |
| #19135503 | 2 |
| #19132683 | 2 |
| C43×#1382 | 2 |
| #13017 | 43 |