Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #11719432 | C2 | semidirect |
| 2. D4×Dic26 | C2 | semidirect |
| 3. C13×#474 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 6. #11718551 | C2 | semidirect |
| 7. #11718535 | C2 | semidirect |
| 8. #11718507 | C2 | semidirect |
| 9. #11718491 | C2 | semidirect |
| 10. #11718420 | C2 | semidirect |
| 61. #6104 | Q8 | semidirect |
| 79. D4×C13 | C2×Q8 | semidirect |
| 92. D52 | C2×Q8 | semidirect |
| 98. Dic26 | D8 | semidirect |
| 101. #1055 | C2×Q8 | semidirect |
| 109. #474 | D13 | semidirect |
| 197. C13 | Q8×D8 | semidirect |
| 208. D4 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719432 | 2 |
| D4×Dic26 | 2 |
| C13×#474 | 2 |
| #11718739 | 2 |
| C4×#6104 | 2 |
| #11718551 | 2 |
| #11718535 | 2 |
| #11718507 | 2 |
| #11718491 | 2 |
| #11718420 | 2 |
| #11718417 | 2 |
| Q8×D8 | 13 |