Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#18011899 | C2 | semidirect |
| 2. #23750007 | C2 | semidirect |
| 3. #23749982 | C2 | semidirect |
| 4. #23749847 | C2 | semidirect |
| 5. #23749840 | C2 | semidirect |
| 6. #23749780 | C2 | semidirect |
| 7. #23749775 | C2 | semidirect |
| 8. #23749763 | C2 | semidirect |
| 10. #23749678 | C2 | semidirect |
| 11. #529×C149 | C2 | semidirect |
| 14. C2×#14558726 | C22 | semidirect |
| 15. C2×#14558724 | C22 | semidirect |
| 24. C4⋊#11924746 | C22 | semidirect |
| 25. #18011834 | C22 | semidirect |
| 26. #18011834 | C22 | semidirect |
| 31. C4×#11924746 | C22 | semidirect |
| 33. #125×C149 | C22 | semidirect |
| 34. #124×C149 | C22 | semidirect |
| 38. C4×Q8×C149 | C22 | semidirect |
| 40. C4×D4×C149 | C22 | semidirect |
| 143. C149 | #3211 | semidirect |
| 145. #529 | D149 | semidirect |
| 163. #125 | C2×D149 | semidirect |
| 168. #124 | C2×D149 | semidirect |
| 172. C4×Q8 | C2×D149 | semidirect |
| 174. C4×D4 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011899 | 2 |
| #23750007 | 2 |
| #23749982 | 2 |
| #23749847 | 2 |
| #23749840 | 2 |
| #23749780 | 2 |
| #23749775 | 2 |
| #23749763 | 2 |
| #23749758 | 2 |
| #23749678 | 2 |
| #529×C149 | 2 |
| #3211 | 149 |