Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
820 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 245 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 |
|---|---|---|
| 3. C22×C4⋊Dic13 | C2 | semidirect |
| 4. C2×#88071 | C2 | semidirect |
| 5. C2×#88071 | C2 | semidirect |
| 6. #11718614 | C2 | direct (N × H) |
| 17. C2×C4⋊Dic13 | C22 | semidirect |
| 18. #88071 | C22 | semidirect |
| 19. #88071 | C22 | semidirect |
| 115. C2×C13 | #397 | semidirect |
| 145. C13 | C2×#397 | semidirect |
| 197. C2 | #11718614 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×C22⋊C4 | 2 |
| C22×C22⋊Dic13 | 2 |
| C22×C4⋊Dic13 | 2 |
| C2×#88071 | 2 |
| #11718614 | 2 |
| C2×#397 | 13 |