Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11718496 | C2 | semidirect |
| 3. D13×C4⋊C8 | C2 | semidirect |
| 4. C13×#331 | C2 | semidirect |
| 5. #11718136 | C2 | semidirect |
| 6. #11718073 | C2 | semidirect |
| 7. #11718073 | C2 | semidirect |
| 81. #331 | D13 | semidirect |
| 143. C13 | #1551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719421 | 2 |
| #11718496 | 2 |
| D13×C4⋊C8 | 2 |
| C13×#331 | 2 |
| #11718136 | 2 |
| #11718073 | 2 |
| #1551 | 13 |