Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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×C13×C22⋊Q8 | C2 | semidirect |
| 3. #11718892 | C2 | semidirect |
| 4. #11718873 | C2 | semidirect |
| 5. #11718655 | C2 | semidirect |
| 6. #11718653 | C2 | semidirect |
| 8. #11718607 | C2 | semidirect |
| 10. C22×Q8×C13 | C22 | semidirect |
| 14. C2×C13×C4⋊C4 | C22 | semidirect |
| 15. C2×C13×C4⋊C4 | C22 | semidirect |
| 23. C2×C4⋊Dic13 | C22 | semidirect |
| 24. C2×#6101 | C22 | semidirect |
| 25. #88071 | C22 | semidirect |
| 26. #88071 | C22 | semidirect |
| 32. C23×D13 | Q8 | semidirect |
| 89. C2×C22⋊Q8 | D13 | semidirect |
| 120. C22×Q8 | C2×D13 | semidirect |
| 126. C2×C4⋊C4 | C2×D13 | semidirect |
| 127. C2×C4⋊C4 | C2×D13 | semidirect |
| 173. C13 | #2626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×C22⋊Q8 | 2 |
| C22×#6103 | 2 |
| #11718892 | 2 |
| #11718873 | 2 |
| #11718655 | 2 |
| #11718653 | 2 |
| #11718616 | 2 |
| #11718607 | 2 |
| #2626 | 13 |