Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. C2×Q16×D13 | C2 | semidirect |
| 3. C2×C13×SD32 | C2 | semidirect |
| 4. C2×#88069 | C2 | semidirect |
| 5. C2×#88067 | C2 | semidirect |
| 6. #11718576 | C2 | direct (N × H) |
| 7. C2×Dic104 | C2 | semidirect |
| 8. C2×#88038 | C2 | semidirect |
| 16. Q16×D13 | C22 | semidirect |
| 22. C13×SD32 | C22 | semidirect |
| 24. #88069 | C22 | semidirect |
| 25. #88067 | C22 | semidirect |
| 27. Dic104 | C22 | semidirect |
| 28. #88038 | C22 | semidirect |
| 89. C2×SD32 | D13 | semidirect |
| 118. SD32 | C2×D13 | semidirect |
| 123. C2×C13 | #510 | semidirect |
| 155. C13 | C2×#510 | semidirect |
| 193. C2 | #11718576 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D13 | 2 |
| C2×#88166 | 2 |
| C2×C13×SD32 | 2 |
| C2×#88069 | 2 |
| C2×#88067 | 2 |
| #11718576 | 2 |
| C2×Dic104 | 2 |
| C2×#88038 | 2 |
| C2×#510 | 13 |