Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 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. C13×#532 | C2 | semidirect |
| 2. C2×#88128 | C2 | semidirect |
| 3. #11718749 | C2 | semidirect |
| 4. #11718734 | C2 | semidirect |
| 5. #11718697 | C2 | semidirect |
| 6. #11718676 | C2 | semidirect |
| 7. #11718586 | C2 | semidirect |
| 12. C13×C4⋊Q8 | C22 | semidirect |
| 13. C13×#127 | C22 | semidirect |
| 18. C4×D4×C13 | C22 | semidirect |
| 20. C2×#6104 | C22 | semidirect |
| 26. #88049 | C22 | semidirect |
| 27. C4⋊#1055 | C22 | semidirect |
| 28. C4×#1055 | C22 | semidirect |
| 75. C2×C4×C13 | D8 | semidirect |
| 89. #532 | D13 | semidirect |
| 119. C4⋊Q8 | C2×D13 | semidirect |
| 124. #127 | C2×D13 | semidirect |
| 129. C4×D4 | C2×D13 | semidirect |
| 171. C13 | #3205 | semidirect |
| 193. C2×C4 | #6104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#532 | 2 |
| C2×#88128 | 2 |
| #11718749 | 2 |
| #11718734 | 2 |
| #11718697 | 2 |
| #11718676 | 2 |
| #11718586 | 2 |
| #3205 | 13 |