Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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. #23750636 | C2 | semidirect |
| 4. #23750591 | C2 | semidirect |
| 5. #23750504 | C2 | semidirect |
| 6. #23750500 | C2 | semidirect |
| 23. #18011828 | C4 | semidirect |
| 24. #18011827 | C4 | semidirect |
| 25. #18011827 | C4 | semidirect |
| 26. #100×C149 | C4 | semidirect |
| 114. C149 | #1931 | semidirect |
| 139. #100 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750636 | 2 |
| #23750617 | 2 |
| C2×#18011973 | 2 |
| #23750591 | 2 |
| #23750504 | 2 |
| #23750500 | 2 |
| #100×D149 | 2 |
| #1931 | 149 |