Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11719623 | C2 | semidirect |
| 3. #11719142 | C2 | semidirect |
| 4. #11719140 | C2 | semidirect |
| 5. #11719138 | C2 | semidirect |
| 6. #11718267 | C2 | semidirect |
| 7. #11718266 | C2 | semidirect |
| 17. C2×C13×D8 | C4 | semidirect |
| 18. C2×#6105 | C4 | semidirect |
| 19. C2×#6104 | C4 | semidirect |
| 22. C2×#6095 | C4 | semidirect |
| 30. C2×D4×C13 | C2×C4 | semidirect |
| 44. C2×Dic26 | C2×C4 | semidirect |
| 59. C2×C8×C13 | C2×C4 | semidirect |
| 62. C2×#1055 | C2×C4 | semidirect |
| 136. C2×D8 | #261 | semidirect |
| 169. C2×D4 | C2×#261 | semidirect |
| 183. C2×C8 | C2×#261 | semidirect |
| 194. C13 | #1904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719623 | 2 |
| C2×#88165 | 2 |
| #11719142 | 2 |
| #11719140 | 2 |
| #11719138 | 2 |
| #11718267 | 2 |
| #11718266 | 2 |
| #1904 | 13 |