Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11718587 | C2 | semidirect |
| 4. #11718044 | C2 | semidirect |
| 14. #88129 | C4 | semidirect |
| 15. C4×D52 | C4 | semidirect |
| 17. #88124 | C4 | semidirect |
| 18. C4×Dic26 | C4 | semidirect |
| 77. C4×C4⋊C4 | D13 | semidirect |
| 148. C13 | #1509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719184 | 2 |
| C4×C13×C4⋊C4 | 2 |
| #11718587 | 2 |
| #11718044 | 2 |
| #11718043 | 2 |
| #1509 | 13 |