Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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. #11718818 | C2 | semidirect |
| 2. C2×#88066 | C2 | semidirect |
| 3. C2×#88038 | C2 | semidirect |
| 4. #11718544 | C2 | semidirect |
| 5. C13×#357 | C2 | semidirect |
| 6. #11718101 | C2 | semidirect |
| 7. #11718082 | C2 | semidirect |
| 39. #6090 | D4 | semidirect |
| 65. #357 | 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 |
|---|---|
| #11718818 | 2 |
| C2×#88066 | 2 |
| C2×#88038 | 2 |
| #11718544 | 2 |
| C13×#357 | 2 |
| #11718101 | 2 |
| #11718082 | 2 |
| #2218 | 13 |