Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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. C4×C13×#41 | C2 | semidirect |
| 2. C2×#88203 | C2 | semidirect |
| 3. C2×#88128 | C2 | semidirect |
| 4. #11718688 | C2 | semidirect |
| 5. #11718676 | C2 | semidirect |
| 6. #11718662 | C2 | semidirect |
| 7. #11718585 | C2 | semidirect |
| 11. C4×Q8×C13 | C22 | semidirect |
| 13. C4×D4×C13 | C22 | semidirect |
| 19. C2×#6106 | C22 | semidirect |
| 20. C2×#6104 | C22 | semidirect |
| 25. #88049 | C22 | semidirect |
| 26. C4⋊#1055 | C22 | semidirect |
| 29. C13×#41 | D4 | semidirect |
| 64. Q8×C13 | C2×D4 | semidirect |
| 67. D4×C13 | C2×D4 | semidirect |
| 87. C4×#41 | D13 | semidirect |
| 104. C4×C13 | AGL(1,ℤ/8) | semidirect |
| 117. C4×Q8 | C2×D13 | semidirect |
| 119. C4×D4 | C2×D13 | semidirect |
| 133. #41 | D52 | semidirect |
| 161. C13 | #3038 | semidirect |
| 168. Q8 | C2×D52 | semidirect |
| 176. D4 | C2×D52 | semidirect |
| 201. C4 | #88203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×#41 | 2 |
| C2×#88203 | 2 |
| C2×#88128 | 2 |
| #11718688 | 2 |
| #11718676 | 2 |
| #11718662 | 2 |
| #11718585 | 2 |
| #3038 | 13 |