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. #23750103 | C2 | semidirect |
| 4. #23749728 | C2 | semidirect |
| 5. #23749710 | C2 | semidirect |
| 6. #23749661 | C2 | semidirect |
| 8. #23749583 | C2 | semidirect |
| 9. #419×C149 | C2 | semidirect |
| 11. C2×#14558723 | C4 | semidirect |
| 16. Q8×Dic149 | C22 | semidirect |
| 23. #18011844 | C22 | semidirect |
| 24. #18011842 | C22 | semidirect |
| 26. #18011821 | C22 | semidirect |
| 27. C8×Dic149 | C22 | semidirect |
| 31. #103×C149 | C22 | semidirect |
| 38. #14558723 | C2×C4 | semidirect |
| 39. #14558723 | C2×C4 | semidirect |
| 40. C2×#11924746 | C2×C4 | semidirect |
| 54. C2×Q8×C149 | C2×C4 | semidirect |
| 103. C149 | #2949 | semidirect |
| 111. #419 | D149 | semidirect |
| 132. #103 | C2×D149 | semidirect |
| 139. C2×Q8 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558723 | 2 |
| #23750103 | 2 |
| #23750099 | 2 |
| #23749728 | 2 |
| #23749710 | 2 |
| #23749661 | 2 |
| #23749631 | 2 |
| #23749583 | 2 |
| #419×C149 | 2 |
| #2949 | 149 |