Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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. #13079352 | C2 | semidirect |
| 2. #13077521 | C2 | semidirect |
| 3. #13070829 | C2 | semidirect |
| 4. #13070788 | C2 | semidirect |
| 5. #13070787 | C2 | semidirect |
| 6. #13070689 | C2 | semidirect |
| 7. #13070560 | C2 | semidirect |
| 8. #13070517 | C2 | semidirect |
| 9. #13070515 | C2 | semidirect |
| 10. #13070427 | C2 | semidirect |
| 11. C11×#2213 | C2 | semidirect |
| 16. C11×#493 | C22 | semidirect |
| 22. #10622765 | C22 | semidirect |
| 32. #10622293 | C22 | semidirect |
| 33. C11×#364 | C22 | semidirect |
| 34. C11×#361 | C22 | semidirect |
| 36. #10622201 | C22 | semidirect |
| 39. #10622151 | C22 | semidirect |
| 40. #10622150 | C22 | semidirect |
| 41. #10622132 | C22 | semidirect |
| 42. #10622101 | C22 | semidirect |
| 114. C11×Q16 | #41 | semidirect |
| 120. C11×D8 | #41 | semidirect |
| 142. Dic44 | #41 | semidirect |
| 143. D88 | #41 | semidirect |
| 163. #2213 | D11 | semidirect |
| 215. #493 | C2×D11 | semidirect |
| 233. #364 | C2×D11 | semidirect |
| 235. #361 | C2×D11 | semidirect |
| 335. Q16 | #4341 | semidirect |
| 346. D8 | #4341 | semidirect |
| 376. C11 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079352 | 2 |
| #13077521 | 2 |
| #13070829 | 2 |
| #13070788 | 2 |
| #13070787 | 2 |
| #13070689 | 2 |
| #13070560 | 2 |
| #13070517 | 2 |
| #13070515 | 2 |
| #13070427 | 2 |
| C11×#2213 | 2 |
| #33688 | 11 |