Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
164 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#88040 | C2 | semidirect |
| 2. C2×C16×D13 | C2 | semidirect |
| 3. #11718548 | C2 | semidirect |
| 5. C13×#367 | C2 | semidirect |
| 6. #11718084 | C2 | semidirect |
| 7. #11718083 | C2 | semidirect |
| 38. C13×C16 | D4 | semidirect |
| 62. #367 | D13 | semidirect |
| 71. C2×D13 | SD32 | semidirect |
| 114. C16 | D52 | semidirect |
| 115. C13 | #2217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88040 | 2 |
| C2×C16×D13 | 2 |
| #11718548 | 2 |
| #11718544 | 2 |
| C13×#367 | 2 |
| #11718084 | 2 |
| #11718083 | 2 |
| #2217 | 13 |