Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C4⋊Dic13 | C2 | semidirect |
| 3. C4×C13×C22⋊C4 | C2 | semidirect |
| 4. #11718619 | C2 | semidirect |
| 5. #11718600 | C2 | semidirect |
| 6. #11718597 | C2 | semidirect |
| 7. #11718335 | C2 | semidirect |
| 76. C4×C22⋊C4 | D13 | semidirect |
| 137. C13 | #2504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88184 | 2 |
| C22×C4⋊Dic13 | 2 |
| C4×C13×C22⋊C4 | 2 |
| #11718619 | 2 |
| #11718600 | 2 |
| #11718597 | 2 |
| #11718335 | 2 |
| #2504 | 13 |