Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
376 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. #11719151 | C2 | semidirect |
| 3. C2×#88115 | C2 | semidirect |
| 4. C2×#88101 | C2 | semidirect |
| 5. C2×#88100 | C2 | semidirect |
| 11. C2×C13×D8 | C4 | semidirect |
| 12. C2×#6104 | C4 | semidirect |
| 15. C2×D104 | C4 | semidirect |
| 71. C8×C13 | C22⋊C4 | semidirect |
| 72. #1055 | C22⋊C4 | semidirect |
| 100. C2×D8 | #261 | semidirect |
| 141. C13 | #1972 | semidirect |
| 167. C8 | C22⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D13 | 2 |
| #11719151 | 2 |
| C2×#88115 | 2 |
| C2×#88101 | 2 |
| C2×#88100 | 2 |
| #1972 | 13 |