Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
648 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 152 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. #11719150 | C2 | semidirect |
| 3. #11719061 | C2 | semidirect |
| 7. C13×#127 | C4 | semidirect |
| 8. #88194 | C4 | semidirect |
| 9. #88128 | C4 | semidirect |
| 15. C2×D4×C13 | C2×C4 | semidirect |
| 16. C2×C22⋊D13 | C2×C4 | semidirect |
| 19. C2×D52 | C2×C4 | semidirect |
| 22. C42×C13 | C2×C4 | semidirect |
| 23. C4×Dic13 | C2×C4 | semidirect |
| 54. #127 | #261 | semidirect |
| 67. C2×D4 | C2×#261 | semidirect |
| 73. C42 | C2×#261 | semidirect |
| 74. C13 | #2380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#127 | 2 |
| #11719150 | 2 |
| #11719061 | 2 |
| #2380 | 13 |