Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11719503 | C2 | semidirect |
| 3. C2×C13×#100 | C2 | semidirect |
| 4. #11718800 | C2 | semidirect |
| 5. #11718149 | C2 | semidirect |
| 11. #88194 | C4 | semidirect |
| 13. #88190 | C4 | semidirect |
| 30. C2×D52 | C2×C4 | semidirect |
| 32. C2×Dic26 | C2×C4 | semidirect |
| 42. C4×Dic13 | C2×C4 | semidirect |
| 43. C4×Dic13 | D4 | semidirect |
| 71. C2×#100 | D13 | semidirect |
| 132. C13 | #1911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719510 | 2 |
| #11719503 | 2 |
| C2×C13×#100 | 2 |
| #11718800 | 2 |
| #11718149 | 2 |
| #1911 | 13 |