Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
284 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 97 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. C4×C4⋊Dic13 | C2 | semidirect |
| 3. #11718586 | C2 | semidirect |
| 4. #11718129 | C2 | semidirect |
| 6. C13×C4⋊Q8 | C4 | semidirect |
| 7. C13×#127 | C4 | semidirect |
| 12. C4×D4×C13 | C4 | semidirect |
| 89. C4⋊Q8 | Dic13 | semidirect |
| 90. #127 | Dic13 | semidirect |
| 95. C4×D4 | Dic13 | semidirect |
| 132. C13 | #1502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#532 | 2 |
| C4×C4⋊Dic13 | 2 |
| #11718586 | 2 |
| #11718129 | 2 |
| #1502 | 13 |