Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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×#88074 | C2 | semidirect |
| 3. #11718137 | C2 | semidirect |
| 4. #11718133 | C2 | semidirect |
| 5. C2×C13×#41 | C4 | semidirect |
| 7. C13×#127 | C4 | semidirect |
| 9. C13×#124 | C4 | semidirect |
| 13. C13×#117 | C4 | semidirect |
| 19. C2×Q8×C13 | C2×C4 | semidirect |
| 25. C2×D4×C13 | C2×C4 | semidirect |
| 35. C42×C13 | C2×C4 | semidirect |
| 36. C42×C13 | C2×C4 | semidirect |
| 85. C2×#41 | Dic13 | semidirect |
| 87. #127 | Dic13 | semidirect |
| 89. #124 | Dic13 | semidirect |
| 93. #117 | Dic13 | semidirect |
| 105. C2×Q8 | C2×Dic13 | semidirect |
| 111. C2×D4 | C2×Dic13 | semidirect |
| 123. C42 | C2×Dic13 | semidirect |
| 124. C42 | C2×Dic13 | semidirect |
| 125. C13 | #2127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#535 | 2 |
| C2×#88074 | 2 |
| #11718137 | 2 |
| #11718133 | 2 |
| #2127 | 13 |