Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 181 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×#88161 | C2 | semidirect |
| 3. C2×C13×#108 | C2 | semidirect |
| 4. C2×#88065 | C2 | semidirect |
| 5. C2×C8×Dic13 | C2 | semidirect |
| 6. #11718556 | C2 | direct (N × H) |
| 13. #88161 | C22 | semidirect |
| 14. C2×Dic52 | C4 | semidirect |
| 15. #88158 | C4 | semidirect |
| 17. C2×D104 | C4 | semidirect |
| 18. C2×#6095 | C4 | semidirect |
| 21. C13×#108 | C22 | semidirect |
| 22. #88065 | C22 | semidirect |
| 23. C8×Dic13 | C22 | semidirect |
| 47. Dic52 | C2×C4 | semidirect |
| 48. D104 | C2×C4 | semidirect |
| 49. #6095 | C2×C4 | semidirect |
| 80. C2×#108 | D13 | semidirect |
| 109. #108 | C2×D13 | semidirect |
| 114. C2×C13 | #443 | semidirect |
| 145. C13 | C2×#443 | semidirect |
| 185. C2 | #11718556 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88161 | 2 |
| C2×#88158 | 2 |
| C2×C13×#108 | 2 |
| C2×#88065 | 2 |
| C2×C8×Dic13 | 2 |
| #11718556 | 2 |
| C2×#443 | 13 |