Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23750196 | C2 | semidirect |
| 3. #23749967 | C2 | semidirect |
| 4. #23749950 | C2 | semidirect |
| 5. #23749871 | C2 | semidirect |
| 6. #23749854 | C2 | semidirect |
| 7. #23749778 | C2 | semidirect |
| 8. #23749766 | C2 | semidirect |
| 9. #408×C149 | C2 | semidirect |
| 10. C22×Dic298 | C22 | semidirect |
| 21. #18011890 | C22 | semidirect |
| 27. #18011870 | C22 | semidirect |
| 28. #18011845 | C22 | semidirect |
| 29. #18011843 | C22 | semidirect |
| 30. #18011836 | C22 | semidirect |
| 31. #18011836 | C22 | semidirect |
| 35. C2×M16×C149 | C22 | semidirect |
| 36. C22×C8×C149 | C22 | semidirect |
| 38. C22⋊C8×C149 | C22 | semidirect |
| 137. C149 | #3200 | semidirect |
| 147. #408 | D149 | semidirect |
| 153. C2×M16 | C2×D149 | semidirect |
| 154. C22×C8 | C2×D149 | semidirect |
| 176. C22⋊C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750196 | 2 |
| #23750189 | 2 |
| #23749967 | 2 |
| #23749950 | 2 |
| #23749871 | 2 |
| #23749854 | 2 |
| #23749778 | 2 |
| #23749766 | 2 |
| #408×C149 | 2 |
| #3200 | 149 |