Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23750170 | C2 | semidirect |
| 2. C2×#18011900 | C2 | semidirect |
| 3. #23750011 | C2 | semidirect |
| 4. #23749986 | C2 | semidirect |
| 5. #23749843 | C2 | semidirect |
| 6. #23749842 | C2 | semidirect |
| 7. #23749764 | C2 | semidirect |
| 8. #23749761 | C2 | semidirect |
| 9. #23749758 | C2 | semidirect |
| 10. #23749679 | C2 | semidirect |
| 11. #448×C149 | C2 | semidirect |
| 14. C2×#14558723 | C22 | semidirect |
| 17. #18011910 | C22 | semidirect |
| 18. #18011907 | C22 | semidirect |
| 26. D4×Dic149 | C22 | semidirect |
| 27. #18011873 | C22 | semidirect |
| 32. #18011840 | C22 | semidirect |
| 33. #18011835 | C22 | semidirect |
| 37. #18011821 | C22 | semidirect |
| 39. C2×SD16×C149 | C22 | semidirect |
| 41. #103×C149 | C22 | semidirect |
| 152. C149 | #3213 | semidirect |
| 161. #448 | D149 | semidirect |
| 169. C2×SD16 | C2×D149 | semidirect |
| 190. #103 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750170 | 2 |
| C2×#18011900 | 2 |
| #23750011 | 2 |
| #23749986 | 2 |
| #23749843 | 2 |
| #23749842 | 2 |
| #23749764 | 2 |
| #23749761 | 2 |
| #23749758 | 2 |
| #23749679 | 2 |
| #448×C149 | 2 |
| #3213 | 149 |