Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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×C4×C8×C13 | C2 | semidirect |
| 4. C2×#88057 | C2 | semidirect |
| 5. C2×#88056 | C2 | semidirect |
| 7. #11718590 | C2 | semidirect |
| 18. C2×#6095 | C4 | semidirect |
| 65. C2×C4×C13 | SD16 | semidirect |
| 88. C8×C13 | C22⋊C4 | semidirect |
| 93. C2×C4×C8 | D13 | semidirect |
| 168. C13 | #1968 | semidirect |
| 192. C2×C4 | #6095 | semidirect |
| 200. C8 | #6103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6095 | 2 |
| C2×C4×C8×C13 | 2 |
| C2×#88061 | 2 |
| C2×#88057 | 2 |
| C2×#88056 | 2 |
| #11718600 | 2 |
| #11718590 | 2 |
| #1968 | 13 |