Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11718499 | C2 | semidirect |
| 3. C13×#334 | C2 | semidirect |
| 4. #11718075 | C2 | semidirect |
| 5. #11718047 | C2 | semidirect |
| 40. C8×C13 | M16 | semidirect |
| 45. #334 | D13 | semidirect |
| 83. C13 | #1594 | semidirect |
| 97. C8 | #6094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718499 | 2 |
| C4×D104 | 2 |
| C13×#334 | 2 |
| #11718075 | 2 |
| #11718047 | 2 |
| #1594 | 13 |