Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 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×#88172 | C2 | semidirect |
| 2. #11719432 | C2 | semidirect |
| 4. C13×#462 | C2 | semidirect |
| 5. #11718848 | C2 | semidirect |
| 6. #11718746 | C2 | semidirect |
| 7. C4×#6107 | C2 | semidirect |
| 8. #11718509 | C2 | semidirect |
| 9. #11718499 | C2 | semidirect |
| 10. #11718473 | C2 | semidirect |
| 11. #11718467 | C2 | semidirect |
| 67. #6107 | D4 | semidirect |
| 120. #462 | D13 | semidirect |
| 137. C4×C13 | #137 | semidirect |
| 218. C13 | #3278 | semidirect |
| 265. C4 | #88172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88172 | 2 |
| #11719432 | 2 |
| #11719282 | 2 |
| C13×#462 | 2 |
| #11718848 | 2 |
| #11718746 | 2 |
| C4×#6107 | 2 |
| #11718509 | 2 |
| #11718499 | 2 |
| #11718473 | 2 |
| #11718467 | 2 |
| #3278 | 13 |