Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
166 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11718256 | C2 | semidirect |
| 5. #11718255 | C2 | semidirect |
| 6. #11718254 | C2 | semidirect |
| 7. #11718253 | C2 | semidirect |
| 59. C8×C13 | M16 | semidirect |
| 61. #1055 | M16 | semidirect |
| 118. C13 | #1569 | semidirect |
| 138. C8 | #6122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719130 | 2 |
| #11719129 | 2 |
| M16×Dic13 | 2 |
| #11718256 | 2 |
| #11718255 | 2 |
| #11718254 | 2 |
| #11718253 | 2 |
| #1569 | 13 |