Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
184 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11718216 | C2 | semidirect |
| 5. C16×#261 | C2 | semidirect |
| 9. #88106 | C4 | semidirect |
| 12. #88098 | C4 | semidirect |
| 14. C2×C13×C16 | C4 | semidirect |
| 15. C2×#6090 | C4 | semidirect |
| 16. C16×D13 | C4 | semidirect |
| 17. C16×D13 | C4 | semidirect |
| 77. C2×C16 | #261 | semidirect |
| 102. C13 | #2108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719089 | 2 |
| D13⋊M32 | 2 |
| C2×C16×D13 | 2 |
| #11718216 | 2 |
| C16×#261 | 2 |
| #2108 | 13 |