Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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. #23750231 | C2 | semidirect |
| 2. #23750002 | C2 | semidirect |
| 3. #23749991 | C2 | semidirect |
| 4. #23749879 | C2 | semidirect |
| 5. #23749862 | C2 | semidirect |
| 6. #23749736 | C2 | semidirect |
| 7. #23749707 | C2 | semidirect |
| 8. #23749579 | C2 | semidirect |
| 9. #499×C149 | C2 | semidirect |
| 84. C149 | #3176 | semidirect |
| 87. #499 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750231 | 2 |
| #23750002 | 2 |
| #23749991 | 2 |
| #23749879 | 2 |
| #23749862 | 2 |
| #23749736 | 2 |
| #23749707 | 2 |
| #23749579 | 2 |
| #499×C149 | 2 |
| #3176 | 149 |