Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
680 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 338 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 |
|---|---|---|
| 3. C2×#88110 | C2 | semidirect |
| 4. #11719047 | C2 | direct (N × H) |
| 8. C2×D13⋊C8 | C4 | semidirect |
| 15. #88110 | C22 | semidirect |
| 26. C2×#1057 | C2×C4 | semidirect |
| 28. D13⋊C8 | C2×C4 | semidirect |
| 50. #1057 | C22×C4 | semidirect |
| 58. C2×D13 | #97 | semidirect |
| 77. C2×C13 | C2×#97 | semidirect |
| 80. D13 | C2×#97 | semidirect |
| 98. C13 | C22×#97 | semidirect |
| 128. C2 | #11719047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D13⋊C8 | 2 |
| C2×C42×D13 | 2 |
| C2×#88110 | 2 |
| #11719047 | 2 |
| C22×#97 | 13 |