Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
232 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 4. #11718280 | C2 | direct (N × H) |
| 7. C2×C13×Q16 | C4 | semidirect |
| 11. Q16×D13 | C4 | semidirect |
| 13. C2×Dic52 | C4 | semidirect |
| 33. C13×Q16 | C2×C4 | semidirect |
| 39. Dic52 | C2×C4 | semidirect |
| 92. C2×Q16 | #261 | semidirect |
| 100. C2×C13 | #358 | semidirect |
| 102. D13 | #358 | semidirect |
| 120. Q16 | C2×#261 | semidirect |
| 130. C13 | C2×#358 | semidirect |
| 169. C2 | #11718280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D13 | 2 |
| C2×#88102 | 2 |
| C2×D13⋊C16 | 2 |
| #11718280 | 2 |
| C2×#358 | 13 |