Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #11719175 | C2 | semidirect |
| 3. C13×#423 | C2 | semidirect |
| 5. #11718782 | C2 | semidirect |
| 6. #11718508 | C2 | semidirect |
| 7. #11718507 | C2 | semidirect |
| 8. #11718503 | C2 | semidirect |
| 22. #88124 | C22 | semidirect |
| 23. #88123 | C22 | semidirect |
| 24. #88123 | C22 | semidirect |
| 27. C13×C4⋊C8 | C22 | semidirect |
| 28. C13×C4⋊C8 | C22 | semidirect |
| 31. #88058 | C22 | semidirect |
| 32. #88057 | C22 | semidirect |
| 40. C2×D52 | Q8 | semidirect |
| 99. #423 | D13 | semidirect |
| 139. C4⋊C8 | C2×D13 | semidirect |
| 140. C4⋊C8 | C2×D13 | semidirect |
| 180. C13 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| #11719175 | 2 |
| C13×#423 | 2 |
| #11718792 | 2 |
| #11718782 | 2 |
| #11718508 | 2 |
| #11718507 | 2 |
| #11718503 | 2 |
| #3077 | 13 |