Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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. C13×#407 | C2 | semidirect |
| 3. C2×#88071 | C2 | semidirect |
| 4. #11718062 | C2 | semidirect |
| 5. #11718059 | C2 | semidirect |
| 8. C2×#6127 | C4 | semidirect |
| 11. #88184 | C4 | semidirect |
| 16. #88180 | C4 | semidirect |
| 17. #88178 | C4 | semidirect |
| 39. C2×D52 | C2×C4 | semidirect |
| 41. C2×Dic26 | C2×C4 | semidirect |
| 49. C4⋊Dic13 | C2×C4 | semidirect |
| 50. C4⋊Dic13 | C2×C4 | semidirect |
| 89. #407 | D13 | semidirect |
| 173. C13 | #1504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719496 | 2 |
| C13×#407 | 2 |
| C2×#88071 | 2 |
| #11718062 | 2 |
| #11718059 | 2 |
| #1504 | 13 |