Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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. #11719111 | C2 | semidirect |
| 3. #11718281 | C2 | semidirect |
| 4. #11718223 | C2 | semidirect |
| 5. C16×#261 | C2 | semidirect |
| 12. C13×Q32 | C4 | semidirect |
| 13. #88068 | C4 | semidirect |
| 14. D208 | C4 | semidirect |
| 54. Q32 | #261 | semidirect |
| 78. C13 | #2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719111 | 2 |
| #11718580 | 2 |
| #11718281 | 2 |
| #11718223 | 2 |
| C16×#261 | 2 |
| #2178 | 13 |