Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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. C13×#466 | C2 | semidirect |
| 2. C2×#88066 | C2 | semidirect |
| 3. #11718776 | C2 | semidirect |
| 4. C2×#88052 | C2 | semidirect |
| 5. #11718154 | C2 | semidirect |
| 6. #11718083 | C2 | semidirect |
| 7. #11718082 | C2 | semidirect |
| 39. #6090 | D4 | semidirect |
| 62. #466 | D13 | semidirect |
| 119. C13 | #2218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#466 | 2 |
| C2×#88066 | 2 |
| #11718776 | 2 |
| C2×#88052 | 2 |
| #11718154 | 2 |
| #11718083 | 2 |
| #11718082 | 2 |
| #2218 | 13 |