Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
160 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 48 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. Q16×#261 | C2 | semidirect |
| 4. #11718280 | C2 | semidirect |
| 6. #11718221 | C2 | semidirect |
| 7. #11718216 | C2 | semidirect |
| 18. C13×SD32 | C4 | semidirect |
| 19. #88068 | C4 | semidirect |
| 20. #88067 | C4 | semidirect |
| 21. #88040 | C4 | semidirect |
| 33. C13×Q16 | C2×C4 | semidirect |
| 37. Dic52 | C2×C4 | semidirect |
| 41. C13×C16 | C2×C4 | semidirect |
| 42. #6090 | C2×C4 | semidirect |
| 88. SD32 | #261 | semidirect |
| 106. Q16 | C2×#261 | semidirect |
| 120. C16 | C2×#261 | semidirect |
| 121. C13 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#261 | 2 |
| D8×#261 | 2 |
| D13×SD32 | 2 |
| #11718280 | 2 |
| #11718276 | 2 |
| #11718221 | 2 |
| #11718216 | 2 |
| #2175 | 13 |