Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#88190 | C2 | semidirect |
| 3. C22×#6095 | C2 | semidirect |
| 4. C2×#88147 | C2 | semidirect |
| 5. C2×C13×#102 | C2 | semidirect |
| 6. C2×#88054 | C2 | semidirect |
| 7. C2×#88050 | C2 | semidirect |
| 8. #11718448 | C2 | direct (N × H) |
| 18. #88190 | C22 | semidirect |
| 25. C2×#6095 | C22 | semidirect |
| 27. #88147 | C22 | semidirect |
| 28. C13×#102 | C22 | semidirect |
| 29. #88054 | C22 | semidirect |
| 30. #88050 | C22 | semidirect |
| 106. C2×#102 | D13 | semidirect |
| 147. #102 | C2×D13 | semidirect |
| 149. C2×C13 | #463 | semidirect |
| 188. C13 | C2×#463 | semidirect |
| 243. C2 | #11718448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88190 | 2 |
| C22×#6104 | 2 |
| C22×#6095 | 2 |
| C2×#88147 | 2 |
| C2×C13×#102 | 2 |
| C2×#88054 | 2 |
| C2×#88050 | 2 |
| #11718448 | 2 |
| C2×#463 | 13 |