Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
994 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 167 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. #13079353 | C2 | semidirect |
| 2. #13079352 | C2 | semidirect |
| 3. #13079067 | C2 | semidirect |
| 4. #13079063 | C2 | semidirect |
| 5. #13068281 | C2 | semidirect |
| 6. #13068246 | C2 | semidirect |
| 7. #13068244 | C2 | semidirect |
| 8. #13068230 | C2 | semidirect |
| 9. #13068202 | C2 | semidirect |
| 10. #13066920 | C2 | semidirect |
| 11. C11×#1721 | C2 | semidirect |
| 18. C11×#493 | C22 | semidirect |
| 20. C11×#486 | C22 | semidirect |
| 26. #10622692 | C22 | semidirect |
| 30. #10622686 | C22 | semidirect |
| 31. #10622683 | C22 | semidirect |
| 35. #10622307 | C22 | semidirect |
| 39. #10622293 | C22 | semidirect |
| 40. C11×#322 | C22 | semidirect |
| 41. #10622092 | C22 | semidirect |
| 42. C8×C11⋊C8 | C22 | semidirect |
| 144. #1721 | D11 | semidirect |
| 183. C8×C11 | AGL(1,ℤ/8) | semidirect |
| 185. C11⋊C8 | AGL(1,ℤ/8) | semidirect |
| 200. #493 | C2×D11 | semidirect |
| 207. #486 | C2×D11 | semidirect |
| 215. #322 | C2×D11 | semidirect |
| 338. C11 | #19745 | semidirect |
| 374. C8 | #66964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079353 | 2 |
| #13079352 | 2 |
| #13079067 | 2 |
| #13079063 | 2 |
| #13068281 | 2 |
| #13068246 | 2 |
| #13068244 | 2 |
| #13068230 | 2 |
| #13068202 | 2 |
| #13066920 | 2 |
| C11×#1721 | 2 |
| #19745 | 11 |