Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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×H(5,𝔽2) | C2 | semidirect |
| 2. #11719648 | C2 | semidirect |
| 3. #11719541 | C2 | semidirect |
| 4. #11719540 | C2 | semidirect |
| 5. #11719527 | C2 | semidirect |
| 6. #11719524 | C2 | semidirect |
| 7. C2×#88186 | C2 | semidirect |
| 9. C13×H(5,𝔽2) | C22 | semidirect |
| 12. C2×C13×#41 | C22 | semidirect |
| 14. C22×D4×C13 | C22 | semidirect |
| 15. #88257 | C22 | semidirect |
| 16. #88256 | C22 | semidirect |
| 20. C2×#6127 | C22 | semidirect |
| 21. #88205 | C22 | semidirect |
| 22. #88204 | C22 | semidirect |
| 23. #88203 | C22 | semidirect |
| 24. #88202 | C22 | semidirect |
| 25. #88196 | C22 | semidirect |
| 26. C2×#6105 | C22 | semidirect |
| 27. #88186 | C22 | semidirect |
| 28. #88186 | C22 | semidirect |
| 29. C2×#6104 | C22 | semidirect |
| 30. C2×#6099 | C22 | semidirect |
| 56. #6127 | C23 | semidirect |
| 57. C2×D52 | C23 | semidirect |
| 59. C2×Dic26 | C23 | semidirect |
| 60. #6107 | C23 | semidirect |
| 61. #6106 | C23 | semidirect |
| 62. #6105 | C23 | semidirect |
| 63. #6104 | C23 | semidirect |
| 65. #6099 | C23 | semidirect |
| 66. C2×#1055 | C23 | semidirect |
| 98. C2×H(5,𝔽2) | D13 | semidirect |
| 122. H(5,𝔽2) | C2×D13 | semidirect |
| 127. C2×#41 | C2×D13 | semidirect |
| 129. C22×D4 | C2×D13 | semidirect |
| 181. C13 | #3585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×H(5,𝔽2) | 2 |
| #11719648 | 2 |
| #11719541 | 2 |
| #11719540 | 2 |
| #11719527 | 2 |
| #11719524 | 2 |
| C2×#88186 | 2 |
| #3585 | 13 |