Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
488 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 178 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. Q16×#261 | C2 | direct (N × H) |
| 15. C2×C13×Q16 | C4 | semidirect |
| 16. C2×#6107 | C4 | semidirect |
| 17. Q16×D13 | C4 | semidirect |
| 19. C2×Dic52 | C4 | semidirect |
| 45. C13×Q16 | C2×C4 | semidirect |
| 47. #6107 | C2×C4 | semidirect |
| 49. Dic52 | C2×C4 | semidirect |
| 57. C2×#261 | Q16 | direct (N × H) |
| 92. #261 | C2×Q16 | direct (N × H) |
| 104. C2×Q16 | #261 | direct (N × H) |
| 116. C2×C13 | C4×Q16 | semidirect |
| 118. D13 | C4×Q16 | semidirect |
| 135. Q16 | C2×#261 | direct (N × H) |
| 149. C13 | C2×C4×Q16 | semidirect |
| 193. C2 | Q16×#261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#261 | 2 |
| C2×Q16×D13 | 2 |
| C2×#88117 | 2 |
| Q16×#261 | 2 |
| C2×#88102 | 2 |
| C2×C8×#261 | 2 |
| C2×C4×Q16 | 13 |