Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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×#18011936 | C2 | semidirect |
| 2. C22×D1192 | C2 | semidirect |
| 3. #23750189 | C2 | semidirect |
| 4. #23750011 | C2 | semidirect |
| 5. #23750010 | C2 | semidirect |
| 6. #23750000 | C2 | semidirect |
| 7. #23749580 | C2 | semidirect |
| 8. C2×#135×C149 | C2 | semidirect |
| 11. C2×#14558723 | C22 | semidirect |
| 15. C2×#14558721 | C22 | semidirect |
| 17. #18011907 | C22 | semidirect |
| 18. #18011900 | C22 | semidirect |
| 22. #18011821 | C22 | semidirect |
| 23. C8×Dic149 | C22 | semidirect |
| 26. C2×Q16×C149 | C22 | semidirect |
| 27. C2×SD16×C149 | C22 | semidirect |
| 28. C2×D8×C149 | C22 | semidirect |
| 40. #14558720 | D4 | semidirect |
| 56. C2×C8×C149 | D4 | semidirect |
| 101. C149 | #3155 | semidirect |
| 104. C2×#135 | D149 | semidirect |
| 115. C2×Q16 | C2×D149 | semidirect |
| 117. C2×SD16 | C2×D149 | semidirect |
| 122. C2×D8 | C2×D149 | semidirect |
| 154. C2×C8 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011936 | 2 |
| C22×D1192 | 2 |
| #23750189 | 2 |
| #23750011 | 2 |
| #23750010 | 2 |
| #23750000 | 2 |
| #23749580 | 2 |
| C2×#135×C149 | 2 |
| #3155 | 149 |