Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 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×#88254 | C2 | semidirect |
| 2. C13×#536 | C2 | semidirect |
| 3. #11719527 | C2 | semidirect |
| 4. C2×#88076 | C2 | semidirect |
| 5. #11718756 | C2 | semidirect |
| 6. #11718723 | C2 | semidirect |
| 7. #11718666 | C2 | semidirect |
| 17. C13×C4⋊Q8 | C22 | semidirect |
| 18. C13×#124 | C22 | semidirect |
| 25. #88196 | C22 | semidirect |
| 26. #88186 | C22 | semidirect |
| 28. #88076 | C22 | semidirect |
| 29. #88045 | C22 | semidirect |
| 106. #536 | D13 | semidirect |
| 140. C4⋊Q8 | C2×D13 | semidirect |
| 141. #124 | C2×D13 | semidirect |
| 194. C13 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88254 | 2 |
| C13×#536 | 2 |
| #11719527 | 2 |
| C2×#88076 | 2 |
| #11718756 | 2 |
| #11718723 | 2 |
| #11718666 | 2 |
| #3020 | 13 |