Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. C13×#500 | C2 | semidirect |
| 3. #11718755 | C2 | semidirect |
| 4. #11718549 | C2 | semidirect |
| 5. #11718548 | C2 | semidirect |
| 6. #11718541 | C2 | semidirect |
| 7. C4×Dic52 | C2 | semidirect |
| 68. #500 | D13 | semidirect |
| 131. C13 | #3342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719437 | 2 |
| C13×#500 | 2 |
| #11718755 | 2 |
| #11718549 | 2 |
| #11718548 | 2 |
| #11718541 | 2 |
| C4×Dic52 | 2 |
| C8×D52 | 2 |
| #3342 | 13 |