Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719290 | C2 | semidirect |
| 2. C4×C13×Q16 | C2 | semidirect |
| 3. #11718852 | C2 | semidirect |
| 4. #11718688 | C2 | semidirect |
| 5. #11718533 | C2 | semidirect |
| 6. #11718480 | C2 | semidirect |
| 8. C8×Dic26 | C2 | semidirect |
| 77. C4×Q16 | D13 | semidirect |
| 137. C13 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719290 | 2 |
| C4×C13×Q16 | 2 |
| #11718852 | 2 |
| #11718688 | 2 |
| #11718533 | 2 |
| #11718480 | 2 |
| #11718356 | 2 |
| C8×Dic26 | 2 |
| #3396 | 13 |