Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#88173 | C2 | semidirect |
| 2. C2×D8×D13 | C2 | semidirect |
| 3. C2×C13×SD32 | C2 | semidirect |
| 4. C2×#88068 | C2 | semidirect |
| 5. C2×#88066 | C2 | semidirect |
| 6. #11718575 | C2 | direct (N × H) |
| 7. C2×D208 | C2 | semidirect |
| 8. C2×#88038 | C2 | semidirect |
| 11. C2×C13×Q16 | C22 | semidirect |
| 16. #88173 | C22 | semidirect |
| 18. D8×D13 | C22 | semidirect |
| 20. C2×D104 | C22 | semidirect |
| 22. C13×SD32 | C22 | semidirect |
| 23. C2×C13×C16 | C22 | semidirect |
| 24. #88068 | C22 | semidirect |
| 25. #88066 | C22 | semidirect |
| 26. C2×#6090 | C22 | semidirect |
| 27. D208 | C22 | semidirect |
| 28. #88038 | C22 | semidirect |
| 43. C13×Q16 | C23 | semidirect |
| 53. D104 | C23 | semidirect |
| 56. C13×C16 | C23 | semidirect |
| 57. #6090 | C23 | semidirect |
| 88. C2×SD32 | D13 | semidirect |
| 110. C2×Q16 | C2×D13 | semidirect |
| 120. SD32 | C2×D13 | semidirect |
| 125. C2×C16 | C2×D13 | semidirect |
| 127. C2×C13 | #509 | semidirect |
| 146. Q16 | C22×D13 | semidirect |
| 160. C16 | C22×D13 | semidirect |
| 161. C13 | C2×#509 | semidirect |
| 205. C2 | #11718575 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88173 | 2 |
| C2×D8×D13 | 2 |
| C2×C13×SD32 | 2 |
| C2×#88068 | 2 |
| C2×#88066 | 2 |
| #11718575 | 2 |
| C2×D208 | 2 |
| C2×#88038 | 2 |
| C2×#509 | 13 |