Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
760 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19135581 | C2 | semidirect |
| 4. #19133115 | C2 | semidirect |
| 5. #19132500 | C2 | semidirect |
| 6. #19132480 | C2 | semidirect |
| 22. C2×#137×C43 | C4 | semidirect |
| 27. C43×#417 | C4 | semidirect |
| 53. C22×Q8×C43 | C2×C4 | semidirect |
| 62. C2×M16×C43 | C2×C4 | semidirect |
| 68. C2×C4⋊C4×C43 | C2×C4 | semidirect |
| 235. C2×#137 | Dic43 | semidirect |
| 242. #417 | Dic43 | semidirect |
| 255. C43 | #9361 | semidirect |
| 261. C22×Q8 | C2×Dic43 | semidirect |
| 272. C2×M16 | C2×Dic43 | semidirect |
| 280. C2×C4⋊C4 | C2×Dic43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19137425 | 2 |
| #19135581 | 2 |
| #19134539 | 2 |
| #19133115 | 2 |
| #19132500 | 2 |
| #19132480 | 2 |
| C43×#3007 | 2 |
| #9361 | 43 |