Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11719423 | C2 | semidirect |
| 2. C13×#493 | C2 | semidirect |
| 3. #11718812 | C2 | semidirect |
| 4. #11718811 | C2 | semidirect |
| 5. D8×Dic13 | C2 | semidirect |
| 6. #11718733 | C2 | semidirect |
| 7. C4×D104 | C2 | semidirect |
| 8. C8×Dic26 | C2 | semidirect |
| 71. Dic26 | D8 | semidirect |
| 73. C8×C13 | #41 | semidirect |
| 77. #493 | D13 | semidirect |
| 145. C13 | #3391 | semidirect |
| 167. C8 | #6129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719423 | 2 |
| C13×#493 | 2 |
| #11718812 | 2 |
| #11718811 | 2 |
| D8×Dic13 | 2 |
| #11718733 | 2 |
| C4×D104 | 2 |
| C8×Dic26 | 2 |
| #3391 | 13 |