Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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. #11719222 | C2 | semidirect |
| 5. #11718125 | C2 | semidirect |
| 6. #11718124 | C2 | semidirect |
| 7. #11718123 | C2 | semidirect |
| 27. C2×Q8×C13 | Q8 | semidirect |
| 29. C2×D4×C13 | Q8 | semidirect |
| 130. C2×Q8 | Dic26 | semidirect |
| 132. C2×D4 | Dic26 | semidirect |
| 157. C13 | #2031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719222 | 2 |
| C13×#410 | 2 |
| #11718897 | 2 |
| C2×#88077 | 2 |
| #11718125 | 2 |
| #11718124 | 2 |
| #11718123 | 2 |
| #2031 | 13 |