Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 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. #23750426 | C2 | semidirect |
| 2. #23749892 | C2 | semidirect |
| 3. #23749792 | C2 | semidirect |
| 4. #23749743 | C2 | semidirect |
| 5. #493×C149 | C2 | semidirect |
| 6. #18011956 | C22 | semidirect |
| 7. #18011937 | C22 | semidirect |
| 12. #18011917 | C22 | semidirect |
| 13. #18011847 | C22 | semidirect |
| 14. #18011839 | C22 | semidirect |
| 15. #18011828 | C22 | semidirect |
| 16. C2×D8×C149 | C22 | semidirect |
| 17. #127×C149 | C22 | semidirect |
| 18. C4×C8×C149 | C22 | semidirect |
| 23. Dic596 | D4 | semidirect |
| 24. #14558725 | D4 | semidirect |
| 26. D1192 | D4 | semidirect |
| 64. C149 | #3292 | semidirect |
| 67. #493 | D149 | semidirect |
| 77. C2×D8 | C2×D149 | semidirect |
| 79. #127 | C2×D149 | semidirect |
| 83. C4×C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750426 | 2 |
| #23749892 | 2 |
| #23749792 | 2 |
| #23749743 | 2 |
| #493×C149 | 2 |
| #3292 | 149 |