Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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. #13070897 | C2 | semidirect |
| 3. #13066822 | C2 | semidirect |
| 4. #13066821 | C2 | semidirect |
| 5. #13066813 | C2 | semidirect |
| 22. C11×Q32 | Q8 | semidirect |
| 24. C11×D16 | Q8 | semidirect |
| 96. Q32 | Dic22 | semidirect |
| 98. D16 | Dic22 | semidirect |
| 129. C11 | #13710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070897 | 2 |
| #13070497 | 2 |
| #13066822 | 2 |
| #13066821 | 2 |
| #13066813 | 2 |
| #13066803 | 2 |
| C11×#1418 | 2 |
| #13710 | 11 |