Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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×#18011933 | C2 | semidirect |
| 2. #23750066 | C2 | semidirect |
| 3. #23750065 | C2 | semidirect |
| 4. #23750061 | C2 | semidirect |
| 5. #23750060 | C2 | semidirect |
| 6. #23750055 | C2 | semidirect |
| 7. C2×#18011851 | C2 | semidirect |
| 8. C2×#135×C149 | C2 | semidirect |
| 13. #18011933 | C22 | semidirect |
| 14. C2×Dic596 | C22 | semidirect |
| 16. C2×D1192 | C22 | semidirect |
| 17. #18011857 | C22 | semidirect |
| 18. #18011855 | C22 | semidirect |
| 19. #18011854 | C22 | semidirect |
| 20. #18011852 | C22 | semidirect |
| 21. #18011851 | C22 | semidirect |
| 22. #18011851 | C22 | semidirect |
| 23. C2×#14558711 | C22 | semidirect |
| 28. #135×C149 | C22 | semidirect |
| 29. C2×Q16×C149 | C22 | semidirect |
| 31. C2×D8×C149 | C22 | semidirect |
| 120. C149 | #3414 | semidirect |
| 123. C2×#135 | D149 | semidirect |
| 139. #135 | C2×D149 | semidirect |
| 141. C2×Q16 | C2×D149 | semidirect |
| 145. C2×D8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011933 | 2 |
| #23750066 | 2 |
| #23750065 | 2 |
| #23750061 | 2 |
| #23750060 | 2 |
| #23750055 | 2 |
| C2×#18011851 | 2 |
| C2×#135×C149 | 2 |
| #3414 | 149 |