Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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. C22×C8×D149 | C2 | semidirect |
| 3. #23750137 | C2 | semidirect |
| 4. #23749867 | C2 | semidirect |
| 5. #23749862 | C2 | semidirect |
| 6. #23749855 | C2 | semidirect |
| 7. #23749619 | C2 | semidirect |
| 8. #427×C149 | C2 | semidirect |
| 12. C2×Dic596 | C22 | semidirect |
| 13. C2×#14558725 | C22 | semidirect |
| 14. C2×D1192 | C22 | semidirect |
| 24. #18011834 | C22 | semidirect |
| 25. #18011831 | C22 | semidirect |
| 28. #107×C149 | C22 | semidirect |
| 29. #106×C149 | C22 | semidirect |
| 54. C2×C8×C149 | D4 | semidirect |
| 94. C2×D149 | #135 | semidirect |
| 106. C149 | #3050 | semidirect |
| 114. #427 | D149 | semidirect |
| 133. #107 | C2×D149 | semidirect |
| 134. #106 | C2×D149 | semidirect |
| 158. C2×C8 | D596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011933 | 2 |
| C22×C8×D149 | 2 |
| #23750137 | 2 |
| #23749867 | 2 |
| #23749862 | 2 |
| #23749855 | 2 |
| #23749619 | 2 |
| #427×C149 | 2 |
| #3050 | 149 |