Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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×C13×#124 | C2 | semidirect |
| 2. C22×#6106 | C2 | semidirect |
| 3. C22×#6104 | C2 | semidirect |
| 4. C2×#88128 | C2 | semidirect |
| 5. #11718719 | C2 | direct (N × H) |
| 6. C2×#88043 | C2 | semidirect |
| 12. C13×#124 | C22 | semidirect |
| 16. C2×#6106 | C22 | semidirect |
| 18. C2×#6104 | C22 | semidirect |
| 21. #88128 | C22 | semidirect |
| 22. #88043 | C22 | semidirect |
| 45. C2×#1055 | D4 | semidirect |
| 70. #1055 | C2×D4 | semidirect |
| 74. C2×#124 | D13 | semidirect |
| 102. #124 | C2×D13 | semidirect |
| 107. C2×C13 | #496 | semidirect |
| 135. C13 | C2×#496 | semidirect |
| 174. C2 | #11718719 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#124 | 2 |
| C22×#6106 | 2 |
| C22×#6104 | 2 |
| C2×#88128 | 2 |
| #11718719 | 2 |
| C2×#88043 | 2 |
| C2×#496 | 13 |