Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
560 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 197 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. C4×C13×C4⋊C4 | C2 | semidirect |
| 3. #11718651 | C2 | semidirect |
| 5. #11718597 | C2 | semidirect |
| 6. C4×C4⋊Dic13 | C2 | semidirect |
| 7. #11718327 | C2 | semidirect |
| 8. #11718325 | C2 | semidirect |
| 20. C4×D52 | C4 | semidirect |
| 81. C4×C4⋊C4 | D13 | semidirect |
| 145. C13 | #2357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| C4×C13×C4⋊C4 | 2 |
| #11718651 | 2 |
| #11718600 | 2 |
| #11718597 | 2 |
| C4×C4⋊Dic13 | 2 |
| #11718327 | 2 |
| #11718325 | 2 |
| #2357 | 13 |