Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
604 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 181 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×#88123 | C2 | semidirect |
| 4. #11718873 | C2 | semidirect |
| 5. #11718635 | C2 | semidirect |
| 6. #11718614 | C2 | semidirect |
| 7. C4×C4⋊Dic13 | C2 | semidirect |
| 92. C4×C13 | #124 | semidirect |
| 140. C13 | #2547 | semidirect |
| 180. C4 | #88190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| C2×#88190 | 2 |
| C2×#88123 | 2 |
| #11718873 | 2 |
| #11718635 | 2 |
| #11718614 | 2 |
| C4×C4⋊Dic13 | 2 |
| #2547 | 13 |