Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. C4×C4⋊Dic13 | C2 | semidirect |
| 4. C2×#88043 | C2 | semidirect |
| 5. #11718121 | C2 | semidirect |
| 9. C4×D4×C13 | C4 | semidirect |
| 16. #88072 | C4 | semidirect |
| 37. C4⋊Dic13 | C2×C4 | semidirect |
| 41. C2×#1055 | C2×C4 | semidirect |
| 51. D4×C13 | C42 | semidirect |
| 94. C4×D4 | Dic13 | semidirect |
| 132. C13 | #1762 | semidirect |
| 141. D4 | C4×Dic13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| C2×#88072 | 2 |
| C4×C4⋊Dic13 | 2 |
| C2×#88043 | 2 |
| #11718121 | 2 |
| #1762 | 13 |