Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. D13×C4⋊Q8 | C2 | semidirect |
| 3. C13×#475 | C2 | semidirect |
| 4. #11718748 | C2 | semidirect |
| 5. #11718681 | C2 | semidirect |
| 6. #11718531 | C2 | semidirect |
| 7. #11718522 | C2 | semidirect |
| 8. #11718507 | C2 | semidirect |
| 9. #11718498 | C2 | semidirect |
| 11. #11718455 | C2 | semidirect |
| 46. #6131 | Q8 | semidirect |
| 87. Q8×C13 | C2×Q8 | semidirect |
| 101. D52 | C2×Q8 | semidirect |
| 119. #475 | D13 | semidirect |
| 219. C13 | #3079 | semidirect |
| 226. Q8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×C4⋊Q8 | 2 |
| C4×#6131 | 2 |
| C13×#475 | 2 |
| #11718748 | 2 |
| #11718681 | 2 |
| #11718531 | 2 |
| #11718522 | 2 |
| #11718507 | 2 |
| #11718498 | 2 |
| #11718464 | 2 |
| #11718455 | 2 |
| #3079 | 13 |