Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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×#88190 | C2 | semidirect |
| 3. C2×#88163 | C2 | semidirect |
| 4. C2×C13×#100 | C2 | semidirect |
| 5. C2×#88065 | C2 | semidirect |
| 6. #11718781 | C2 | semidirect |
| 7. #11718147 | C2 | semidirect |
| 53. C2×Dic26 | D4 | semidirect |
| 57. C13×M16 | D4 | semidirect |
| 66. C4×Dic13 | D4 | semidirect |
| 113. C2×#100 | D13 | semidirect |
| 190. M16 | C22⋊D13 | semidirect |
| 200. C13 | #2004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719510 | 2 |
| C2×#88190 | 2 |
| C2×#88163 | 2 |
| C2×C13×#100 | 2 |
| C2×#88065 | 2 |
| #11718781 | 2 |
| #11718147 | 2 |
| #2004 | 13 |