Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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×#88038 | C2 | semidirect |
| 3. D13×#108 | C2 | semidirect |
| 4. C13×#359 | C2 | semidirect |
| 5. #11718159 | C2 | semidirect |
| 6. #11718102 | C2 | semidirect |
| 7. #11718089 | C2 | semidirect |
| 20. C2×C13×C16 | C22 | semidirect |
| 21. C13×#108 | C22 | semidirect |
| 23. #88059 | C22 | semidirect |
| 24. C2×#6090 | C22 | semidirect |
| 96. #359 | D13 | semidirect |
| 125. C2×C16 | C2×D13 | semidirect |
| 128. #108 | C2×D13 | semidirect |
| 168. C13 | #2143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#135 | 2 |
| C2×#88038 | 2 |
| D13×#108 | 2 |
| C13×#359 | 2 |
| #11718159 | 2 |
| #11718102 | 2 |
| #11718089 | 2 |
| #2143 | 13 |