Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
500 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 225 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. #41×Dic13 | C2 | semidirect |
| 3. #11718894 | C2 | semidirect |
| 4. Q16×Dic13 | C2 | semidirect |
| 5. SD16×Dic13 | C2 | semidirect |
| 6. D8×Dic13 | C2 | semidirect |
| 7. #11718767 | C2 | semidirect |
| 8. C2×C8×Dic13 | C2 | semidirect |
| 10. C13×#135 | C4 | semidirect |
| 30. C13×#41 | C2×C4 | semidirect |
| 38. C13×Q16 | C2×C4 | semidirect |
| 39. C13×SD16 | C2×C4 | semidirect |
| 40. C13×D8 | C2×C4 | semidirect |
| 41. C2×C8×C13 | C2×C4 | semidirect |
| 96. Dic13 | #135 | direct (N × H) |
| 98. #135 | Dic13 | direct (N × H) |
| 122. #41 | C2×Dic13 | semidirect |
| 130. Q16 | C2×Dic13 | semidirect |
| 131. SD16 | C2×Dic13 | semidirect |
| 132. D8 | C2×Dic13 | semidirect |
| 135. C2×C8 | C2×Dic13 | semidirect |
| 147. C13 | C4×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#135 | 2 |
| #41×Dic13 | 2 |
| #11718894 | 2 |
| Q16×Dic13 | 2 |
| SD16×Dic13 | 2 |
| D8×Dic13 | 2 |
| #11718767 | 2 |
| C2×C8×Dic13 | 2 |
| C4×#135 | 13 |