Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#88165 | C2 | semidirect |
| 2. #11719421 | C2 | semidirect |
| 3. D13×#127 | C2 | semidirect |
| 4. C13×#493 | C2 | semidirect |
| 5. #11718815 | C2 | semidirect |
| 6. #11718737 | C2 | semidirect |
| 7. #11718734 | C2 | semidirect |
| 8. #11718354 | C2 | semidirect |
| 9. C4×#6094 | C2 | semidirect |
| 13. C2×C13×D8 | C22 | semidirect |
| 15. C13×#127 | C22 | semidirect |
| 19. #88190 | C22 | semidirect |
| 21. C2×#6105 | C22 | semidirect |
| 22. C2×#6104 | C22 | semidirect |
| 24. C2×#6095 | C22 | semidirect |
| 28. #88123 | C22 | semidirect |
| 29. C4×C8×C13 | C22 | semidirect |
| 30. #88055 | C22 | semidirect |
| 31. C4×#1055 | C22 | semidirect |
| 60. #6094 | D4 | semidirect |
| 86. C8×C13 | C2×D4 | semidirect |
| 87. #1055 | C2×D4 | semidirect |
| 93. #493 | D13 | semidirect |
| 107. C4×C13 | AGL(1,ℤ/8) | semidirect |
| 119. C2×D8 | C2×D13 | semidirect |
| 126. #127 | C2×D13 | semidirect |
| 133. C4×C8 | C2×D13 | semidirect |
| 169. C13 | #3151 | semidirect |
| 195. C8 | D4×D13 | semidirect |
| 209. C4 | #88165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88165 | 2 |
| #11719421 | 2 |
| D13×#127 | 2 |
| C13×#493 | 2 |
| #11718815 | 2 |
| #11718737 | 2 |
| #11718734 | 2 |
| #11718354 | 2 |
| C4×#6094 | 2 |
| #3151 | 13 |