Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
402 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 3. (C2×#261)⋊Q8 | C2 | semidirect |
| 4. C2×#88117 | C2 | semidirect |
| 6. #11718265 | C2 | semidirect |
| 7. (C2×#261)⋊C8 | C2 | semidirect |
| 18. C2×C13×SD16 | C4 | semidirect |
| 19. C2×#6106 | C4 | semidirect |
| 20. C2×#6105 | C4 | semidirect |
| 23. C2×#6095 | C4 | semidirect |
| 37. C2×Q8×C13 | C2×C4 | semidirect |
| 52. C2×Dic26 | C2×C4 | semidirect |
| 64. C2×C8×C13 | C2×C4 | semidirect |
| 67. C2×#1055 | C2×C4 | semidirect |
| 93. C2×#261 | SD16 | semidirect |
| 161. C2×SD16 | #261 | semidirect |
| 190. C2×Q8 | C2×#261 | semidirect |
| 217. C2×C8 | C2×#261 | semidirect |
| 225. C13 | #1877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#261 | 2 |
| C2×SD16×D13 | 2 |
| (C2×#261)⋊Q8 | 2 |
| C2×#88117 | 2 |
| C2×#88115 | 2 |
| #11718265 | 2 |
| (C2×#261)⋊C8 | 2 |
| #1877 | 13 |