Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
676 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 173 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×#88129 | C2 | semidirect |
| 3. C2×C4×Dic26 | C2 | semidirect |
| 4. C4×C13×C4⋊C4 | C2 | semidirect |
| 5. #11718649 | C2 | semidirect |
| 6. #11718600 | C2 | semidirect |
| 7. #11718333 | C2 | semidirect |
| 40. C2×Dic26 | D4 | semidirect |
| 81. C4×C4⋊C4 | D13 | semidirect |
| 95. C4×C13 | #124 | semidirect |
| 145. C13 | #2548 | semidirect |
| 185. C4 | #88129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88129 | 2 |
| C2×#88128 | 2 |
| C2×C4×Dic26 | 2 |
| C4×C13×C4⋊C4 | 2 |
| #11718649 | 2 |
| #11718600 | 2 |
| #11718333 | 2 |
| #2548 | 13 |