Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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×#88038 | C2 | semidirect |
| 3. C13×C22⋊C16 | C2 | semidirect |
| 4. C22⋊#6090 | C2 | semidirect |
| 5. #11718099 | C2 | semidirect |
| 14. C2×C13×C16 | C22 | semidirect |
| 15. C2×#6090 | C22 | semidirect |
| 66. C22⋊C16 | D13 | semidirect |
| 69. C22×C13 | M32 | semidirect |
| 77. C2×D13 | M32 | semidirect |
| 93. C2×C16 | C2×D13 | semidirect |
| 121. C13 | #2112 | semidirect |
| 154. C22 | #88038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D13 | 2 |
| C2×#88038 | 2 |
| C13×C22⋊C16 | 2 |
| C22⋊#6090 | 2 |
| #11718099 | 2 |
| #2112 | 13 |