Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #13079354 | C2 | semidirect |
| 2. #13070830 | C2 | semidirect |
| 3. #13070787 | C2 | semidirect |
| 4. #13070692 | C2 | semidirect |
| 5. #13070562 | C2 | semidirect |
| 6. #13070514 | C2 | semidirect |
| 7. #13070428 | C2 | semidirect |
| 8. C11×#2956 | C2 | semidirect |
| 23. #10622324 | C22 | semidirect |
| 24. #10622308 | C22 | semidirect |
| 26. #10622293 | C22 | semidirect |
| 29. #10622133 | C22 | semidirect |
| 30. #10622132 | C22 | semidirect |
| 31. #10622104 | C22 | semidirect |
| 32. #10622101 | C22 | semidirect |
| 90. C11×Q16 | #41 | semidirect |
| 94. C11×D8 | #41 | semidirect |
| 119. #2956 | D11 | semidirect |
| 258. Q16 | #4339 | semidirect |
| 264. D8 | #4339 | semidirect |
| 286. C11 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079354 | 2 |
| #13070830 | 2 |
| #13070787 | 2 |
| #13070692 | 2 |
| #13070562 | 2 |
| #13070514 | 2 |
| #13070428 | 2 |
| C11×#2956 | 2 |
| #33688 | 11 |