Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C13×#125 | C2 | semidirect |
| 3. #11718729 | C2 | direct (N × H) |
| 4. C2×#88050 | C2 | semidirect |
| 6. C2×C4×#1055 | C2 | semidirect |
| 10. C13×#125 | C22 | semidirect |
| 18. #88050 | C22 | semidirect |
| 20. C4×#1055 | C22 | semidirect |
| 59. C2×#125 | D13 | semidirect |
| 80. #125 | C2×D13 | semidirect |
| 90. C2×C13 | #488 | semidirect |
| 113. C13 | C2×#488 | semidirect |
| 144. C2 | #11718729 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#125 | 2 |
| C2×#88129 | 2 |
| #11718729 | 2 |
| C2×#88050 | 2 |
| C2×#88049 | 2 |
| C2×C4×#1055 | 2 |
| C2×#488 | 13 |