Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. #11719182 | C2 | semidirect |
| 2. C2×#88128 | C2 | semidirect |
| 3. C13×#431 | C2 | semidirect |
| 4. #11718504 | C2 | semidirect |
| 5. #11718393 | C2 | semidirect |
| 6. #11718356 | C2 | semidirect |
| 7. #11718355 | C2 | semidirect |
| 15. C2×D104 | C22 | semidirect |
| 21. #88128 | C22 | semidirect |
| 23. C4×D52 | C22 | semidirect |
| 24. #88123 | C22 | semidirect |
| 25. C13×C4⋊C8 | C22 | semidirect |
| 27. C4×C8×C13 | C22 | semidirect |
| 28. #88061 | C22 | semidirect |
| 68. C2×C4×C13 | D8 | semidirect |
| 95. #431 | D13 | semidirect |
| 131. C4⋊C8 | C2×D13 | semidirect |
| 134. C4×C8 | C2×D13 | semidirect |
| 171. C13 | #3205 | semidirect |
| 193. C2×C4 | D104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719182 | 2 |
| C2×#88128 | 2 |
| C13×#431 | 2 |
| #11718504 | 2 |
| #11718393 | 2 |
| #11718356 | 2 |
| #11718355 | 2 |
| #3205 | 13 |