Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 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. #23750349 | C2 | semidirect |
| 2. #23750290 | C2 | semidirect |
| 3. #23749986 | C2 | semidirect |
| 4. #23749918 | C2 | semidirect |
| 5. #23749902 | C2 | semidirect |
| 7. #23749827 | C2 | semidirect |
| 8. #23749755 | C2 | semidirect |
| 9. #23749728 | C2 | semidirect |
| 11. #487×C149 | C2 | semidirect |
| 122. C149 | #3367 | semidirect |
| 127. #487 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750349 | 2 |
| #23750290 | 2 |
| #23749986 | 2 |
| #23749918 | 2 |
| #23749902 | 2 |
| #23749843 | 2 |
| #23749827 | 2 |
| #23749755 | 2 |
| #23749728 | 2 |
| C4×D1192 | 2 |
| #487×C149 | 2 |
| #3367 | 149 |