Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23752769 | C2 | semidirect |
| 2. #23752571 | C2 | semidirect |
| 3. #23752566 | C2 | semidirect |
| 4. #23752221 | C2 | semidirect |
| 6. C4×#14558988 | C2 | semidirect |
| 9. #18012739 | C22 | semidirect |
| 10. #18012731 | C22 | semidirect |
| 14. #18012663 | C22 | semidirect |
| 16. #18012650 | C22 | semidirect |
| 17. C4×C151⋊C8 | C22 | semidirect |
| 83. C151 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752769 | 2 |
| #23752571 | 2 |
| #23752566 | 2 |
| #23752221 | 2 |
| #23752217 | 2 |
| C4×#14558988 | 2 |
| C2×#124×C151 | 2 |
| #3140 | 151 |