Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23749652 | C2 | semidirect |
| 5. C2×#18011822 | C2 | semidirect |
| 6. #23749389 | C2 | semidirect |
| 7. #339×C149 | C2 | semidirect |
| 14. #18011834 | C4 | semidirect |
| 15. #18011831 | C4 | semidirect |
| 90. C149 | #1938 | semidirect |
| 98. #339 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23749652 | 2 |
| C2×#18011839 | 2 |
| #23749619 | 2 |
| #23749593 | 2 |
| C2×#18011822 | 2 |
| #23749389 | 2 |
| #339×C149 | 2 |
| #1938 | 149 |