Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. C13×#367 | C2 | semidirect |
| 5. #11718096 | C2 | semidirect |
| 6. #11718082 | C2 | semidirect |
| 7. #11718081 | C2 | semidirect |
| 19. #88038 | C4 | semidirect |
| 33. C13×C16 | C2×C4 | semidirect |
| 34. #6090 | C2×C4 | semidirect |
| 53. #367 | D13 | semidirect |
| 97. C16 | C4×D13 | semidirect |
| 98. C13 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88038 | 2 |
| #11718541 | 2 |
| D13×#107 | 2 |
| C13×#367 | 2 |
| #11718096 | 2 |
| #11718082 | 2 |
| #11718081 | 2 |
| #2159 | 13 |