Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
162 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 162 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 |
|---|---|---|
| 2. C2×#88052 | C2 | semidirect |
| 3. C2×#88038 | C2 | semidirect |
| 4. C13×C22⋊C16 | C2 | semidirect |
| 5. #11718099 | C2 | semidirect |
| 6. #11718093 | C2 | semidirect |
| 7. C16×Dic13 | C2 | semidirect |
| 39. #6090 | D4 | semidirect |
| 63. C22⋊C16 | D13 | semidirect |
| 77. Dic13 | M32 | semidirect |
| 115. C13 | #2169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C22⋊D13 | 2 |
| C2×#88052 | 2 |
| C2×#88038 | 2 |
| C13×C22⋊C16 | 2 |
| #11718099 | 2 |
| #11718093 | 2 |
| C16×Dic13 | 2 |
| #2169 | 13 |