Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×#88170 | C2 | semidirect |
| 2. #11719423 | C2 | semidirect |
| 3. #11719282 | C2 | semidirect |
| 4. C13×#460 | C2 | semidirect |
| 5. #11718833 | C2 | semidirect |
| 6. #11718734 | C2 | semidirect |
| 7. C4×#6107 | C2 | semidirect |
| 8. #11718509 | C2 | semidirect |
| 9. #11718495 | C2 | semidirect |
| 10. #11718442 | C2 | semidirect |
| 11. #11718436 | C2 | semidirect |
| 69. #6107 | D4 | semidirect |
| 124. #460 | D13 | semidirect |
| 142. C4×C13 | #135 | semidirect |
| 224. C13 | #3287 | semidirect |
| 276. C4 | #88170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88170 | 2 |
| #11719423 | 2 |
| #11719282 | 2 |
| C13×#460 | 2 |
| #11718833 | 2 |
| #11718734 | 2 |
| C4×#6107 | 2 |
| #11718509 | 2 |
| #11718495 | 2 |
| #11718442 | 2 |
| #11718436 | 2 |
| #3287 | 13 |