Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23752767 | C2 | semidirect |
| 3. #23752606 | C2 | semidirect |
| 4. #23752582 | C2 | semidirect |
| 5. #23752574 | C2 | semidirect |
| 6. #23752471 | C2 | semidirect |
| 8. #23752306 | C2 | semidirect |
| 9. #23752299 | C2 | semidirect |
| 10. #23752164 | C2 | semidirect |
| 11. #501×C151 | C2 | semidirect |
| 129. C151 | #3172 | semidirect |
| 133. #501 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| #23752747 | 2 |
| #23752606 | 2 |
| #23752582 | 2 |
| #23752574 | 2 |
| #23752471 | 2 |
| #23752459 | 2 |
| #23752306 | 2 |
| #23752299 | 2 |
| #23752164 | 2 |
| #501×C151 | 2 |
| #3172 | 151 |