Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×Q16×D13 | C2 | semidirect |
| 4. C13×#462 | C2 | semidirect |
| 5. #11718847 | C2 | semidirect |
| 6. #11718753 | C2 | semidirect |
| 7. C4×#6107 | C2 | semidirect |
| 8. #11718510 | C2 | semidirect |
| 10. #11718474 | C2 | semidirect |
| 11. #11718469 | C2 | semidirect |
| 66. #6107 | D4 | semidirect |
| 98. D52 | Q16 | semidirect |
| 118. #462 | D13 | semidirect |
| 126. C2×D13 | C2×Q16 | semidirect |
| 131. C4×C13 | C2×Q16 | semidirect |
| 212. C13 | D4×Q16 | semidirect |
| 254. C4 | Q16×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D13 | 2 |
| #11719432 | 2 |
| Q8×D52 | 2 |
| C13×#462 | 2 |
| #11718847 | 2 |
| #11718753 | 2 |
| C4×#6107 | 2 |
| #11718510 | 2 |
| #11718495 | 2 |
| #11718474 | 2 |
| #11718469 | 2 |
| D4×Q16 | 13 |