Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #23749723 | C2 | semidirect |
| 4. C4×#14558723 | C2 | semidirect |
| 5. #23749661 | C2 | semidirect |
| 6. #23749634 | C2 | semidirect |
| 8. #23749581 | C2 | semidirect |
| 9. #519×C149 | C2 | semidirect |
| 11. C2×#14558723 | C4 | semidirect |
| 20. #18011844 | C22 | semidirect |
| 21. #18011842 | C22 | semidirect |
| 22. #18011835 | C22 | semidirect |
| 24. #18011822 | C22 | semidirect |
| 25. C4×#11924746 | C22 | semidirect |
| 28. C4×Q8×C149 | C22 | semidirect |
| 38. #14558723 | C2×C4 | semidirect |
| 39. #14558723 | C2×C4 | semidirect |
| 41. C2×#11924746 | C2×C4 | semidirect |
| 51. C2×Q8×C149 | C2×C4 | semidirect |
| 103. C149 | #2949 | semidirect |
| 106. #519 | D149 | semidirect |
| 122. C4×Q8 | 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 |
| #23750099 | 2 |
| #23749723 | 2 |
| C4×#14558723 | 2 |
| #23749661 | 2 |
| #23749634 | 2 |
| #23749629 | 2 |
| #23749581 | 2 |
| #519×C149 | 2 |
| #2949 | 149 |