Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
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×C11×H(5,𝔽2) | C2 | semidirect |
| 2. #10623453 | C2 | semidirect |
| 3. #10623367 | C2 | semidirect |
| 4. #10623366 | C2 | semidirect |
| 5. #10623353 | C2 | semidirect |
| 6. #10623350 | C2 | semidirect |
| 7. C2×#66985 | C2 | semidirect |
| 9. C11×H(5,𝔽2) | C22 | semidirect |
| 12. C2×C11×#41 | C22 | semidirect |
| 14. C22×D4×C11 | C22 | semidirect |
| 15. #67043 | C22 | semidirect |
| 16. #67042 | C22 | semidirect |
| 20. C2×#4339 | C22 | semidirect |
| 21. #67004 | C22 | semidirect |
| 22. #67003 | C22 | semidirect |
| 23. #67002 | C22 | semidirect |
| 24. #67001 | C22 | semidirect |
| 25. #66995 | C22 | semidirect |
| 26. C2×#4324 | C22 | semidirect |
| 27. #66985 | C22 | semidirect |
| 28. #66985 | C22 | semidirect |
| 29. C2×#4323 | C22 | semidirect |
| 30. C2×#4318 | C22 | semidirect |
| 56. #4339 | C23 | semidirect |
| 57. C2×D44 | C23 | semidirect |
| 59. C2×Dic22 | C23 | semidirect |
| 60. #4326 | C23 | semidirect |
| 61. #4325 | C23 | semidirect |
| 62. #4324 | C23 | semidirect |
| 63. #4323 | C23 | semidirect |
| 65. #4318 | C23 | semidirect |
| 66. C2×C11⋊C8 | C23 | semidirect |
| 98. C2×H(5,𝔽2) | D11 | semidirect |
| 122. H(5,𝔽2) | C2×D11 | semidirect |
| 127. C2×#41 | C2×D11 | semidirect |
| 129. C22×D4 | C2×D11 | semidirect |
| 181. C11 | #3585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×H(5,𝔽2) | 2 |
| #10623453 | 2 |
| #10623367 | 2 |
| #10623366 | 2 |
| #10623353 | 2 |
| #10623350 | 2 |
| C2×#66985 | 2 |
| #3585 | 11 |