Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
560 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 160 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. (C2×#261)⋊Q8 | C2 | semidirect |
| 4. #11719071 | C2 | semidirect |
| 5. C22⋊C4×#261 | C2 | semidirect |
| 6. #11719057 | C2 | semidirect |
| 15. C13×#124 | C4 | semidirect |
| 16. #88201 | C4 | semidirect |
| 17. #88190 | C4 | semidirect |
| 18. #88139 | C4 | semidirect |
| 20. #88129 | C4 | semidirect |
| 31. C2×Q8×C13 | C2×C4 | semidirect |
| 42. C2×Dic26 | C2×C4 | semidirect |
| 43. C2×Dic26 | C2×C4 | semidirect |
| 49. C13×C22⋊C4 | C2×C4 | semidirect |
| 50. C42×C13 | C2×C4 | semidirect |
| 51. C22⋊Dic13 | C2×C4 | semidirect |
| 52. #6103 | C2×C4 | semidirect |
| 53. #6103 | C2×C4 | semidirect |
| 54. C4×Dic13 | C2×C4 | semidirect |
| 55. C4×Dic13 | C2×C4 | semidirect |
| 120. #124 | #261 | semidirect |
| 143. C2×Q8 | C2×#261 | semidirect |
| 162. C22⋊C4 | C2×#261 | semidirect |
| 167. C42 | C2×#261 | semidirect |
| 168. C13 | #2372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#124 | 2 |
| (C2×#261)⋊Q8 | 2 |
| #11719150 | 2 |
| #11719071 | 2 |
| C22⋊C4×#261 | 2 |
| #11719057 | 2 |
| #2372 | 13 |