Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 3. #11718785 | C2 | semidirect |
| 4. M16×Dic13 | C2 | semidirect |
| 6. C13×#344 | C2 | semidirect |
| 7. #11718124 | C2 | semidirect |
| 17. #88064 | C4 | semidirect |
| 18. #88063 | C4 | semidirect |
| 82. #344 | D13 | semidirect |
| 146. C13 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88065 | 2 |
| #11718793 | 2 |
| #11718785 | 2 |
| M16×Dic13 | 2 |
| #11718666 | 2 |
| C13×#344 | 2 |
| #11718124 | 2 |
| #1932 | 13 |