Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #23750102 | C2 | semidirect |
| 4. #23749724 | C2 | semidirect |
| 5. #23749712 | C2 | semidirect |
| 6. #23749633 | C2 | semidirect |
| 8. #23749580 | C2 | semidirect |
| 9. #427×C149 | C2 | semidirect |
| 12. C2×#14558725 | C4 | semidirect |
| 17. #18011876 | C22 | semidirect |
| 23. #18011834 | C22 | semidirect |
| 25. #18011821 | C22 | semidirect |
| 26. C8×Dic149 | C22 | semidirect |
| 30. #107×C149 | C22 | semidirect |
| 31. #106×C149 | C22 | semidirect |
| 35. C2×Dic298 | C2×C4 | semidirect |
| 43. #14558725 | C2×C4 | semidirect |
| 44. #14558725 | C2×C4 | semidirect |
| 54. C2×C8×C149 | C2×C4 | semidirect |
| 103. C149 | #2949 | semidirect |
| 110. #427 | D149 | semidirect |
| 130. #107 | C2×D149 | semidirect |
| 131. #106 | C2×D149 | semidirect |
| 152. C2×C8 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558725 | 2 |
| #23750102 | 2 |
| #23750099 | 2 |
| #23749724 | 2 |
| #23749712 | 2 |
| #23749633 | 2 |
| #23749629 | 2 |
| #23749580 | 2 |
| #427×C149 | 2 |
| #2949 | 149 |