Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
456 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 156 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. #23750657 | C2 | semidirect |
| 2. #23750646 | C2 | semidirect |
| 3. #23750595 | C2 | semidirect |
| 4. D149⋊(C22⋊C8) | C2 | semidirect |
| 6. C2×#14558745 | C22 | semidirect |
| 7. C2×D149⋊C8 | C22 | semidirect |
| 8. C4⋊#11924753 | C22 | semidirect |
| 9. #18011968 | C22 | semidirect |
| 11. C22⋊#11924753 | C22 | semidirect |
| 12. #18011966 | C22 | semidirect |
| 48. C22×D149 | M16 | semidirect |
| 95. C149 | #2973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750657 | 2 |
| #23750646 | 2 |
| #23750595 | 2 |
| D149⋊(C22⋊C8) | 2 |
| C2×#18011871 | 2 |
| #2973 | 149 |