Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 2. #11718685 | C2 | semidirect |
| 4. C13×Q8⋊C8 | C2 | semidirect |
| 5. #11718071 | C2 | semidirect |
| 7. #11718046 | C2 | semidirect |
| 61. #1055 | M16 | semidirect |
| 66. Q8⋊C8 | D13 | semidirect |
| 118. C13 | #1592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6106 | 2 |
| #11718685 | 2 |
| #11718499 | 2 |
| C13×Q8⋊C8 | 2 |
| #11718071 | 2 |
| #11718051 | 2 |
| #11718046 | 2 |
| #1592 | 13 |