Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#6106 | C2 | semidirect |
| 3. C13×#391 | C2 | semidirect |
| 4. C2×#88049 | C2 | semidirect |
| 5. #11718116 | C2 | semidirect |
| 22. C2×Q8×C13 | D4 | semidirect |
| 41. C2×#1055 | D4 | semidirect |
| 58. C2×C4×C13 | SD16 | semidirect |
| 72. #391 | D13 | semidirect |
| 111. C2×Q8 | D52 | semidirect |
| 131. C13 | #2014 | semidirect |
| 152. C2×C4 | #6106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6106 | 2 |
| C2×#88128 | 2 |
| C13×#391 | 2 |
| C2×#88049 | 2 |
| #11718116 | 2 |
| #2014 | 13 |