Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
224 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#88062 | C2 | semidirect |
| 4. #11718658 | C2 | semidirect |
| 6. C13×#339 | C2 | semidirect |
| 7. #11718116 | C2 | semidirect |
| 18. #88050 | C4 | semidirect |
| 19. #88050 | C4 | semidirect |
| 20. #88049 | C4 | semidirect |
| 21. #88049 | C4 | semidirect |
| 89. #339 | D13 | semidirect |
| 160. C13 | #1929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718790 | 2 |
| C2×#88062 | 2 |
| #11718663 | 2 |
| #11718658 | 2 |
| C2×#88045 | 2 |
| C13×#339 | 2 |
| #11718116 | 2 |
| #1929 | 13 |