Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 402 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. #23750203 | C2 | semidirect |
| 2. #23749961 | C2 | semidirect |
| 3. #23749939 | C2 | semidirect |
| 4. #23749871 | C2 | semidirect |
| 5. #23749866 | C2 | semidirect |
| 6. #23749861 | C2 | semidirect |
| 7. #23749789 | C2 | semidirect |
| 8. #23749772 | C2 | semidirect |
| 9. #408×C149 | C2 | semidirect |
| 119. C149 | #3203 | semidirect |
| 129. #408 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750203 | 2 |
| #23749961 | 2 |
| #23749939 | 2 |
| #23749871 | 2 |
| #23749866 | 2 |
| #23749861 | 2 |
| #23749789 | 2 |
| #23749772 | 2 |
| #408×C149 | 2 |
| #3203 | 149 |