Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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×C13×C16 | C2 | semidirect |
| 2. #11718777 | C2 | semidirect |
| 4. C2×#88040 | C2 | semidirect |
| 5. #11718101 | C2 | semidirect |
| 6. #11718097 | C2 | semidirect |
| 7. #11718095 | C2 | semidirect |
| 39. C13×C16 | D4 | semidirect |
| 59. C22×C16 | D13 | semidirect |
| 67. C22×C13 | SD32 | semidirect |
| 114. C16 | C22⋊D13 | semidirect |
| 115. C13 | #2217 | semidirect |
| 138. C22 | #88040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×C16 | 2 |
| #11718777 | 2 |
| #11718776 | 2 |
| C2×#88040 | 2 |
| #11718101 | 2 |
| #11718097 | 2 |
| #11718095 | 2 |
| #2217 | 13 |