Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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. Q16×Dic13 | C2 | semidirect |
| 4. C13×#358 | C2 | semidirect |
| 6. #11718094 | C2 | semidirect |
| 7. #11718081 | C2 | semidirect |
| 15. #88068 | C4 | semidirect |
| 24. C13×Q16 | C2×C4 | semidirect |
| 36. #6090 | C2×C4 | semidirect |
| 57. #358 | D13 | semidirect |
| 91. Q16 | C4×D13 | semidirect |
| 104. C13 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic13 | 2 |
| C2×#88068 | 2 |
| #11718533 | 2 |
| C13×#358 | 2 |
| #11718101 | 2 |
| #11718094 | 2 |
| #11718081 | 2 |
| #2175 | 13 |