Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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. C13×#529 | C2 | semidirect |
| 2. C2×#88128 | C2 | semidirect |
| 3. #11718728 | C2 | semidirect |
| 4. #11718719 | C2 | semidirect |
| 5. #11718707 | C2 | semidirect |
| 6. #11718697 | C2 | semidirect |
| 7. #11718688 | C2 | semidirect |
| 8. #11718676 | C2 | semidirect |
| 9. #11718587 | C2 | semidirect |
| 14. C13×#125 | C22 | semidirect |
| 15. C13×#124 | C22 | semidirect |
| 19. C4×Q8×C13 | C22 | semidirect |
| 21. C4×D4×C13 | C22 | semidirect |
| 24. C2×#6106 | C22 | semidirect |
| 25. C2×#6104 | C22 | semidirect |
| 31. #88049 | C22 | semidirect |
| 32. #88049 | C22 | semidirect |
| 33. C4⋊#1055 | C22 | semidirect |
| 34. #88043 | C22 | semidirect |
| 103. #529 | D13 | semidirect |
| 141. #125 | C2×D13 | semidirect |
| 142. #124 | C2×D13 | semidirect |
| 146. C4×Q8 | C2×D13 | semidirect |
| 148. C4×D4 | C2×D13 | semidirect |
| 198. C13 | #3217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#529 | 2 |
| C2×#88128 | 2 |
| #11718728 | 2 |
| #11718719 | 2 |
| #11718707 | 2 |
| #11718697 | 2 |
| #11718688 | 2 |
| #11718676 | 2 |
| #11718587 | 2 |
| #3217 | 13 |