Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
324 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 103 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. #13070415 | C2 | semidirect |
| 2. #13068747 | C2 | semidirect |
| 3. #13066628 | C2 | semidirect |
| 7. C11×#499 | C4 | semidirect |
| 8. C11×#495 | C4 | semidirect |
| 13. C4×C11×Q16 | C4 | semidirect |
| 15. C4×C11×D8 | C4 | semidirect |
| 125. #499 | Dic11 | semidirect |
| 126. #495 | Dic11 | semidirect |
| 131. C4×Q16 | Dic11 | semidirect |
| 133. C4×D8 | Dic11 | semidirect |
| 231. C11 | #11855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070415 | 2 |
| #13068747 | 2 |
| #13066628 | 2 |
| #13066625 | 2 |
| C11×#3168 | 2 |
| #11855 | 11 |