Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 4. #11718218 | C2 | semidirect |
| 5. #11718217 | C2 | semidirect |
| 9. #88106 | C4 | semidirect |
| 15. D13⋊C16 | C4 | semidirect |
| 16. C13×M32 | C4 | semidirect |
| 17. #88052 | C4 | semidirect |
| 19. C16×D13 | C4 | semidirect |
| 35. #6092 | C2×C4 | semidirect |
| 36. C13×C16 | C2×C4 | semidirect |
| 37. #6090 | C2×C4 | semidirect |
| 77. M32 | #261 | semidirect |
| 87. D13 | #347 | semidirect |
| 105. C16 | C2×#261 | semidirect |
| 106. C13 | C2×#347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88100 | 2 |
| D13⋊M32 | 2 |
| D13×M32 | 2 |
| #11718218 | 2 |
| #11718217 | 2 |
| C2×#347 | 13 |