Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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×#88077 | C2 | semidirect |
| 3. C42×Dic13 | C2 | semidirect |
| 4. #11718585 | C2 | semidirect |
| 6. C13×C4⋊Q8 | C4 | semidirect |
| 7. C13×#127 | C4 | semidirect |
| 8. C13×#124 | C4 | semidirect |
| 34. C4×Dic13 | D4 | semidirect |
| 68. C4×C13 | #104 | semidirect |
| 75. C4⋊Q8 | Dic13 | semidirect |
| 76. #127 | Dic13 | semidirect |
| 77. #124 | Dic13 | semidirect |
| 109. C13 | #1962 | semidirect |
| 137. C4 | #88077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#532 | 2 |
| C2×#88077 | 2 |
| C42×Dic13 | 2 |
| #11718585 | 2 |
| #1962 | 13 |