Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
3464 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 429 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. C22×C13×C22⋊C4 | C2 | semidirect |
| 3. C22×C22⋊Dic13 | C2 | semidirect |
| 4. C22×#6103 | C2 | semidirect |
| 5. #11718616 | C2 | direct (N × H) |
| 10. C24×D13 | C4 | semidirect |
| 13. C23×C4×C13 | C22 | semidirect |
| 14. C23×Dic13 | C22 | semidirect |
| 16. C2×C13×C22⋊C4 | C22 | semidirect |
| 18. C2×C22⋊Dic13 | C22 | semidirect |
| 20. C2×#6103 | C22 | semidirect |
| 38. C23×D13 | C2×C4 | semidirect |
| 43. C22×C4×C13 | C23 | semidirect |
| 46. C22×Dic13 | C23 | semidirect |
| 55. C23×C13 | C22⋊C4 | semidirect |
| 76. C22×D13 | C22⋊C4 | semidirect |
| 88. C22×C22⋊C4 | D13 | semidirect |
| 96. C22×C13 | C2×C22⋊C4 | semidirect |
| 109. C2×D13 | C2×C22⋊C4 | semidirect |
| 120. C23×C4 | C2×D13 | semidirect |
| 126. C2×C22⋊C4 | C2×D13 | semidirect |
| 128. C2×C13 | #379 | semidirect |
| 159. C22×C4 | C22×D13 | semidirect |
| 163. C13 | C2×#379 | semidirect |
| 183. C23 | #6103 | semidirect |
| 212. C22 | C2×#6103 | semidirect |
| 222. C2 | #11718616 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D13 | 2 |
| C22×C13×C22⋊C4 | 2 |
| C22×C22⋊Dic13 | 2 |
| C22×#6103 | 2 |
| #11718616 | 2 |
| C2×#379 | 13 |