Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #11719450 | C2 | semidirect |
| 3. C13×#430 | C2 | semidirect |
| 4. C2×#88065 | C2 | semidirect |
| 5. M16×Dic13 | C2 | semidirect |
| 6. #11718556 | C2 | semidirect |
| 7. #11718555 | C2 | semidirect |
| 13. #88163 | C4 | semidirect |
| 14. #88162 | C4 | semidirect |
| 15. #88161 | C22 | semidirect |
| 19. C13×#108 | C22 | semidirect |
| 20. #88065 | C22 | semidirect |
| 21. #88065 | C22 | semidirect |
| 22. #88055 | C22 | semidirect |
| 23. C8×Dic13 | C22 | semidirect |
| 44. Dic52 | C2×C4 | semidirect |
| 45. D104 | C2×C4 | semidirect |
| 46. #6095 | C2×C4 | semidirect |
| 75. #430 | D13 | semidirect |
| 100. #108 | C2×D13 | semidirect |
| 134. C13 | #2956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719453 | 2 |
| #11719450 | 2 |
| C13×#430 | 2 |
| C2×#88065 | 2 |
| M16×Dic13 | 2 |
| #11718556 | 2 |
| #11718555 | 2 |
| #2956 | 13 |