Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23750256 | C2 | semidirect |
| 3. #23749927 | C2 | semidirect |
| 4. #23749923 | C2 | semidirect |
| 5. #23749913 | C2 | semidirect |
| 6. #23749903 | C2 | semidirect |
| 7. #23749665 | C2 | semidirect |
| 8. #23749663 | C2 | semidirect |
| 9. #23749651 | C2 | semidirect |
| 14. #18011910 | C22 | semidirect |
| 16. #18011902 | C22 | semidirect |
| 26. #18011845 | C22 | semidirect |
| 27. #18011845 | C22 | semidirect |
| 28. #18011844 | C22 | semidirect |
| 29. #18011843 | C22 | semidirect |
| 30. #18011843 | C22 | semidirect |
| 31. #18011842 | C22 | semidirect |
| 32. #18011840 | C22 | semidirect |
| 33. #18011840 | C22 | semidirect |
| 66. C2×D4×C149 | Q8 | semidirect |
| 124. C149 | #3081 | semidirect |
| 170. C2×D4 | Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750256 | 2 |
| #23750100 | 2 |
| #23749927 | 2 |
| #23749923 | 2 |
| #23749913 | 2 |
| #23749903 | 2 |
| #23749665 | 2 |
| #23749663 | 2 |
| #23749651 | 2 |
| #23749630 | 2 |
| C2×#102×C149 | 2 |
| #3081 | 149 |