Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
568 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×C4×Dic26 | C2 | semidirect |
| 3. C13×#376 | C2 | semidirect |
| 4. C4×#6103 | C2 | semidirect |
| 5. #11718335 | C2 | semidirect |
| 6. #11718334 | C2 | semidirect |
| 8. #11718320 | C2 | semidirect |
| 83. #376 | D13 | semidirect |
| 146. C13 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| C2×C4×Dic26 | 2 |
| C13×#376 | 2 |
| C4×#6103 | 2 |
| #11718335 | 2 |
| #11718334 | 2 |
| #11718333 | 2 |
| #11718320 | 2 |
| #2398 | 13 |