Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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×#88161 | C2 | semidirect |
| 2. C22×#6094 | C2 | semidirect |
| 4. C13×#424 | C2 | semidirect |
| 5. #11718787 | C2 | semidirect |
| 6. #11718771 | C2 | semidirect |
| 7. #11718658 | C2 | semidirect |
| 8. #11718499 | C2 | semidirect |
| 9. #11718497 | C2 | semidirect |
| 21. C2×#6094 | C22 | semidirect |
| 22. C2×C8×D13 | C22 | semidirect |
| 28. C13×C4⋊C8 | C22 | semidirect |
| 30. #88060 | C22 | semidirect |
| 31. #88043 | C22 | semidirect |
| 32. C4×#1055 | C22 | semidirect |
| 58. C2×#1055 | D4 | semidirect |
| 99. #424 | D13 | semidirect |
| 136. C4⋊C8 | C2×D13 | semidirect |
| 179. C13 | #2930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88161 | 2 |
| C22×#6094 | 2 |
| #11719229 | 2 |
| C13×#424 | 2 |
| #11718787 | 2 |
| #11718771 | 2 |
| #11718658 | 2 |
| #11718499 | 2 |
| #11718497 | 2 |
| #2930 | 13 |