Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
726 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 200 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. #11719631 | C2 | semidirect |
| 3. D13⋊#131 | C2 | semidirect |
| 4. #11719165 | C2 | semidirect |
| 5. #11719164 | C2 | semidirect |
| 6. #11719153 | C2 | semidirect |
| 7. C2×#88117 | C2 | semidirect |
| 8. C13×2−1+4 | C4 | semidirect |
| 10. #88257 | C4 | semidirect |
| 11. #88257 | C4 | semidirect |
| 16. #88254 | C4 | semidirect |
| 35. C13×#41 | C2×C4 | semidirect |
| 37. C2×Q8×C13 | C2×C4 | semidirect |
| 39. #6131 | C2×C4 | semidirect |
| 45. Q8×D13 | C2×C4 | semidirect |
| 51. #6129 | C2×C4 | semidirect |
| 60. #6127 | C2×C4 | semidirect |
| 66. C2×Dic26 | C2×C4 | semidirect |
| 147. 2−1+4 | #261 | semidirect |
| 188. #41 | C2×#261 | semidirect |
| 200. C2×Q8 | C2×#261 | semidirect |
| 219. C13 | #2898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×2−1+4 | 2 |
| #11719631 | 2 |
| D13⋊#131 | 2 |
| #11719165 | 2 |
| #11719164 | 2 |
| #11719153 | 2 |
| C2×#88117 | 2 |
| #2898 | 13 |