Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750175 | C2 | semidirect |
| 2. #23750159 | C2 | semidirect |
| 3. #23749926 | C2 | semidirect |
| 4. #23749921 | C2 | semidirect |
| 5. #23749916 | C2 | semidirect |
| 6. #23749861 | C2 | semidirect |
| 7. #23749854 | C2 | semidirect |
| 8. #23749841 | C2 | semidirect |
| 9. #23749826 | C2 | semidirect |
| 10. #23749821 | C2 | semidirect |
| 11. C2×C4⋊C8×C149 | C2 | semidirect |
| 141. C149 | #3247 | semidirect |
| 153. C2×C4⋊C8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23750159 | 2 |
| #23749926 | 2 |
| #23749921 | 2 |
| #23749916 | 2 |
| #23749861 | 2 |
| #23749854 | 2 |
| #23749841 | 2 |
| #23749826 | 2 |
| #23749821 | 2 |
| C2×C4⋊C8×C149 | 2 |
| #3247 | 149 |