Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11719224 | C2 | semidirect |
| 3. C13×#424 | C2 | semidirect |
| 5. #11718782 | C2 | semidirect |
| 7. #11718767 | C2 | semidirect |
| 8. #11718508 | C2 | semidirect |
| 9. #11718508 | C2 | semidirect |
| 10. #11718507 | C2 | semidirect |
| 11. #11718503 | C2 | semidirect |
| 27. #88124 | C22 | semidirect |
| 28. #88123 | C22 | semidirect |
| 29. C13×C4⋊C8 | C22 | semidirect |
| 30. C13×C4⋊C8 | C22 | semidirect |
| 35. #88058 | C22 | semidirect |
| 36. #88058 | C22 | semidirect |
| 37. #88058 | C22 | semidirect |
| 38. #88057 | C22 | semidirect |
| 39. #88057 | C22 | semidirect |
| 40. #88057 | C22 | semidirect |
| 46. C2×D52 | Q8 | semidirect |
| 110. #424 | D13 | semidirect |
| 154. C4⋊C8 | C2×D13 | semidirect |
| 155. C4⋊C8 | C2×D13 | semidirect |
| 199. C13 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719226 | 2 |
| #11719224 | 2 |
| C13×#424 | 2 |
| #11718792 | 2 |
| #11718782 | 2 |
| C2×#88061 | 2 |
| #11718767 | 2 |
| #11718508 | 2 |
| #11718507 | 2 |
| #11718503 | 2 |
| #3081 | 13 |