Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q8×D88 | C2 | semidirect |
| 2. #13070839 | C2 | semidirect |
| 4. #13066672 | C2 | semidirect |
| 5. Q8⋊(C11⋊C16) | C2 | semidirect |
| 6. #13066576 | C2 | semidirect |
| 7. C11×#1668 | C2 | semidirect |
| 84. D88 | SD16 | semidirect |
| 90. #1668 | D11 | semidirect |
| 97. Q8×C11 | D16 | semidirect |
| 222. C11 | #12352 | semidirect |
| 229. Q8 | #66890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D88 | 2 |
| #13070839 | 2 |
| #13070648 | 2 |
| #13066672 | 2 |
| Q8⋊(C11⋊C16) | 2 |
| #13066576 | 2 |
| C11×#1668 | 2 |
| #12352 | 11 |