Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×C13×SD32 | C2 | semidirect |
| 2. #11718842 | C2 | semidirect |
| 3. C2×#88068 | C2 | semidirect |
| 5. C2×#88067 | C2 | semidirect |
| 6. C2×#88040 | C2 | semidirect |
| 7. C16×Dic13 | C2 | semidirect |
| 42. C13×C16 | D4 | semidirect |
| 43. #6090 | D4 | semidirect |
| 66. C2×SD32 | D13 | semidirect |
| 79. Dic13 | SD32 | semidirect |
| 119. C16 | C22⋊D13 | semidirect |
| 120. C13 | #2248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×SD32 | 2 |
| #11718842 | 2 |
| C2×#88068 | 2 |
| #11718812 | 2 |
| C2×#88067 | 2 |
| C2×#88040 | 2 |
| C16×Dic13 | 2 |
| #2248 | 13 |