Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23750180 | C2 | semidirect |
| 3. #23750020 | C2 | semidirect |
| 4. #23750019 | C2 | semidirect |
| 5. #23749987 | C2 | semidirect |
| 6. #23749850 | C2 | semidirect |
| 7. #23749846 | C2 | semidirect |
| 8. #23749782 | C2 | semidirect |
| 10. #23749680 | C2 | semidirect |
| 11. #489×C149 | C2 | semidirect |
| 14. C2×Dic596 | C22 | semidirect |
| 15. C2×#14558726 | C22 | semidirect |
| 18. #18011911 | C22 | semidirect |
| 28. #18011876 | C22 | semidirect |
| 33. #18011840 | C22 | semidirect |
| 34. #18011834 | C22 | semidirect |
| 37. #18011822 | C22 | semidirect |
| 38. C4⋊Q8×C149 | C22 | semidirect |
| 40. #103×C149 | C22 | semidirect |
| 42. #97×C149 | C22 | semidirect |
| 142. C149 | #3215 | semidirect |
| 149. #489 | D149 | semidirect |
| 162. C4⋊Q8 | C2×D149 | semidirect |
| 180. #103 | C2×D149 | semidirect |
| 185. #97 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750180 | 2 |
| #124×D149 | 2 |
| #23750020 | 2 |
| #23750019 | 2 |
| #23749987 | 2 |
| #23749850 | 2 |
| #23749846 | 2 |
| #23749782 | 2 |
| #23749777 | 2 |
| #23749680 | 2 |
| #489×C149 | 2 |
| #3215 | 149 |