Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23750179 | C2 | semidirect |
| 3. #23749921 | C2 | semidirect |
| 4. #23749920 | C2 | semidirect |
| 5. #23749903 | C2 | semidirect |
| 6. #23749870 | C2 | semidirect |
| 7. #23749868 | C2 | semidirect |
| 8. #23749828 | C2 | semidirect |
| 9. #23749822 | C2 | semidirect |
| 10. #23749647 | C2 | semidirect |
| 11. #460×C149 | C2 | semidirect |
| 137. C149 | #3254 | semidirect |
| 148. #460 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750179 | 2 |
| #23750173 | 2 |
| #23749921 | 2 |
| #23749920 | 2 |
| #23749903 | 2 |
| #23749870 | 2 |
| #23749868 | 2 |
| #23749828 | 2 |
| #23749822 | 2 |
| #23749647 | 2 |
| #460×C149 | 2 |
| #3254 | 149 |