Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 3. C8×Dic26 | C2 | semidirect |
| 4. C13×#322 | C2 | semidirect |
| 6. #11718050 | C2 | semidirect |
| 7. #11718048 | C2 | semidirect |
| 54. Dic26 | M16 | semidirect |
| 68. #322 | D13 | semidirect |
| 118. C13 | #1588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6095 | 2 |
| #11718349 | 2 |
| C8×Dic26 | 2 |
| C13×#322 | 2 |
| #11718051 | 2 |
| #11718050 | 2 |
| #11718048 | 2 |
| #1588 | 13 |