Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. C13×#467 | C2 | semidirect |
| 3. C2×#88069 | C2 | semidirect |
| 4. C2×#88068 | C2 | semidirect |
| 5. C22⋊#6090 | C2 | semidirect |
| 6. #11718084 | C2 | semidirect |
| 7. #11718083 | C2 | semidirect |
| 71. #467 | D13 | semidirect |
| 132. C13 | #2189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88158 | 2 |
| C13×#467 | 2 |
| C2×#88069 | 2 |
| C2×#88068 | 2 |
| C22⋊#6090 | 2 |
| #11718084 | 2 |
| #11718083 | 2 |
| #2189 | 13 |