Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23752831 | C2 | semidirect |
| 2. #23752617 | C2 | semidirect |
| 3. #23752571 | C2 | semidirect |
| 4. #23752455 | C2 | semidirect |
| 5. #23752450 | C2 | semidirect |
| 7. #23752313 | C2 | semidirect |
| 8. Q16×Dic151 | C2 | semidirect |
| 9. D8×Dic151 | C2 | semidirect |
| 10. #23752166 | C2 | semidirect |
| 11. #495×C151 | C2 | semidirect |
| 117. C151 | #3175 | semidirect |
| 121. #495 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752831 | 2 |
| #23752617 | 2 |
| #23752571 | 2 |
| #23752455 | 2 |
| #23752450 | 2 |
| #23752445 | 2 |
| #23752313 | 2 |
| Q16×Dic151 | 2 |
| D8×Dic151 | 2 |
| #23752166 | 2 |
| #495×C151 | 2 |
| #3175 | 151 |