Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 1. C22×Dic52 | C2 | semidirect |
| 4. C2×#88123 | C2 | semidirect |
| 5. C2×C13×#97 | C2 | semidirect |
| 6. #11718376 | C2 | direct (N × H) |
| 15. C2×Dic52 | C22 | semidirect |
| 21. #88123 | C22 | semidirect |
| 22. C13×#97 | C22 | semidirect |
| 73. C2×#97 | D13 | semidirect |
| 100. #97 | C2×D13 | semidirect |
| 101. C2×C13 | #497 | semidirect |
| 128. C13 | C2×#497 | semidirect |
| 162. C2 | #11718376 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic52 | 2 |
| C22×#6095 | 2 |
| C2×#88129 | 2 |
| C2×#88123 | 2 |
| C2×C13×#97 | 2 |
| #11718376 | 2 |
| C2×#497 | 13 |