Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 4. #11719110 | C2 | semidirect |
| 5. Q16×#261 | C2 | semidirect |
| 15. C2×C13×Q16 | C4 | semidirect |
| 16. C2×#6107 | C4 | semidirect |
| 17. Q16×D13 | C4 | semidirect |
| 18. Q16×D13 | C4 | semidirect |
| 21. C2×Dic52 | C4 | semidirect |
| 111. C2×Q16 | #261 | semidirect |
| 160. C13 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719627 | 2 |
| C2×Q16×D13 | 2 |
| #11719153 | 2 |
| #11719110 | 2 |
| Q16×#261 | 2 |
| #11719092 | 2 |
| #11719089 | 2 |
| #2950 | 13 |