Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
928 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 274 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. (C2×#261)⋊Q8 | C2 | direct (N × H) |
| 8. C22×Q8×C13 | C4 | semidirect |
| 11. C2×Q8×D13 | C4 | semidirect |
| 15. C22×Dic26 | C4 | semidirect |
| 16. C22×Dic26 | C4 | semidirect |
| 27. C22×#261 | Q8 | semidirect |
| 31. C2×Q8×C13 | C2×C4 | semidirect |
| 49. C2×Dic26 | C2×C4 | semidirect |
| 50. C2×Dic26 | C2×C4 | semidirect |
| 67. C2×#261 | C2×Q8 | semidirect |
| 114. C22×Q8 | #261 | semidirect |
| 124. C2×C13 | #391 | semidirect |
| 127. D13 | #391 | semidirect |
| 140. C2×Q8 | C2×#261 | semidirect |
| 162. C13 | C2×#391 | semidirect |
| 216. C2 | (C2×#261)⋊Q8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D13 | 2 |
| C22×C4⋊#261 | 2 |
| C22×C4×#261 | 2 |
| (C2×#261)⋊Q8 | 2 |
| C2×(C2×#261)⋊C4 | 2 |
| C2×#391 | 13 |