Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11719423 | C2 | semidirect |
| 2. D4×Dic26 | C2 | semidirect |
| 3. C13×#459 | C2 | semidirect |
| 4. #11718811 | C2 | semidirect |
| 5. D8×Dic13 | C2 | semidirect |
| 6. #11718731 | C2 | semidirect |
| 7. C4×#6104 | C2 | semidirect |
| 8. #11718507 | C2 | semidirect |
| 9. #11718491 | C2 | semidirect |
| 10. #11718421 | C2 | semidirect |
| 11. #11718420 | C2 | semidirect |
| 84. D4×C13 | #41 | semidirect |
| 103. Dic26 | D8 | semidirect |
| 114. #459 | D13 | semidirect |
| 206. C13 | #3358 | semidirect |
| 222. D4 | #6129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719423 | 2 |
| D4×Dic26 | 2 |
| C13×#459 | 2 |
| #11718811 | 2 |
| D8×Dic13 | 2 |
| #11718731 | 2 |
| C4×#6104 | 2 |
| #11718507 | 2 |
| #11718491 | 2 |
| #11718421 | 2 |
| #11718420 | 2 |
| #3358 | 13 |