Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
230 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 230 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. C2×#88158 | C2 | semidirect |
| 2. #11718776 | C2 | semidirect |
| 3. C2×#88040 | C2 | semidirect |
| 4. C2×D208 | C2 | semidirect |
| 5. C13×C22⋊C16 | C2 | semidirect |
| 6. #11718101 | C2 | semidirect |
| 7. #11718095 | C2 | semidirect |
| 39. Dic52 | D4 | semidirect |
| 43. D104 | D4 | semidirect |
| 75. C22⋊C16 | D13 | semidirect |
| 136. C13 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88158 | 2 |
| #11718776 | 2 |
| C2×#88040 | 2 |
| C2×D208 | 2 |
| C13×C22⋊C16 | 2 |
| #11718101 | 2 |
| #11718095 | 2 |
| #2186 | 13 |