Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11718130 | C2 | direct (N × H) |
| 5. C22×Q8×C13 | C4 | semidirect |
| 10. C13×C22⋊Q8 | C4 | semidirect |
| 13. C2×C13×C4⋊C4 | C4 | semidirect |
| 23. C2×Q8×C13 | C2×C4 | semidirect |
| 40. C13×C4⋊C4 | C2×C4 | semidirect |
| 98. C22×Q8 | Dic13 | semidirect |
| 104. C22⋊Q8 | Dic13 | semidirect |
| 107. C2×C4⋊C4 | Dic13 | semidirect |
| 116. C2×C13 | #328 | semidirect |
| 123. C2×Q8 | C2×Dic13 | semidirect |
| 142. C4⋊C4 | C2×Dic13 | semidirect |
| 145. C13 | C2×#328 | semidirect |
| 197. C2 | #11718130 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×C22⋊Q8 | 2 |
| C2×#88071 | 2 |
| C2×C22⋊#1055 | 2 |
| #11718130 | 2 |
| C2×#328 | 13 |