Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23750340 | C2 | semidirect |
| 2. #23750280 | C2 | semidirect |
| 3. #23749976 | C2 | semidirect |
| 4. #23749967 | C2 | semidirect |
| 5. #23749916 | C2 | semidirect |
| 6. #23749854 | C2 | semidirect |
| 7. #23749831 | C2 | semidirect |
| 8. #23749772 | C2 | semidirect |
| 9. C4×D1192 | C2 | semidirect |
| 10. #23749622 | C2 | semidirect |
| 11. C8×D4×C149 | C2 | semidirect |
| 130. C149 | #3303 | semidirect |
| 141. C8×D4 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750340 | 2 |
| #23750280 | 2 |
| #23749976 | 2 |
| #23749967 | 2 |
| #23749916 | 2 |
| #23749854 | 2 |
| #23749831 | 2 |
| #23749772 | 2 |
| C4×D1192 | 2 |
| #23749622 | 2 |
| C8×D4×C149 | 2 |
| #3303 | 149 |