Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#88178 | C2 | semidirect |
| 3. C4×C13×C22⋊C4 | C2 | semidirect |
| 5. #11718604 | C2 | semidirect |
| 6. #11718601 | C2 | semidirect |
| 7. #11718335 | C2 | semidirect |
| 8. #11718334 | C2 | semidirect |
| 12. C22×Dic26 | C22 | semidirect |
| 14. C2×C42×C13 | C22 | semidirect |
| 21. C2×C4⋊Dic13 | C22 | semidirect |
| 23. C2×#6101 | C22 | semidirect |
| 24. C13×#95 | C22 | semidirect |
| 25. #88071 | C22 | semidirect |
| 26. #88071 | C22 | semidirect |
| 92. C4×C22⋊C4 | D13 | semidirect |
| 127. C2×C42 | C2×D13 | semidirect |
| 130. #95 | C2×D13 | semidirect |
| 164. C13 | #2561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6103 | 2 |
| C2×#88178 | 2 |
| C4×C13×C22⋊C4 | 2 |
| #11718616 | 2 |
| #11718604 | 2 |
| #11718601 | 2 |
| #11718335 | 2 |
| #11718334 | 2 |
| #2561 | 13 |