Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#88162 | C2 | semidirect |
| 2. C22×D104 | C2 | semidirect |
| 3. C2×#88155 | C2 | semidirect |
| 4. C2×C13×#108 | C2 | semidirect |
| 5. C2×#88063 | C2 | semidirect |
| 6. #11718558 | C2 | direct (N × H) |
| 13. #88162 | C22 | semidirect |
| 18. C2×D104 | C22 | semidirect |
| 21. #88155 | C22 | semidirect |
| 24. C13×#108 | C22 | semidirect |
| 25. #88063 | C22 | semidirect |
| 92. C2×#108 | D13 | semidirect |
| 126. #108 | C2×D13 | semidirect |
| 130. C2×C13 | #472 | semidirect |
| 166. C13 | C2×#472 | semidirect |
| 215. C2 | #11718558 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88162 | 2 |
| C22×D104 | 2 |
| C2×#88155 | 2 |
| C2×C13×#108 | 2 |
| C2×#88063 | 2 |
| #11718558 | 2 |
| C2×#472 | 13 |