Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23752762 | C2 | semidirect |
| 2. #23752746 | C2 | semidirect |
| 3. #23752596 | C2 | semidirect |
| 4. #23752567 | C2 | semidirect |
| 5. #23752423 | C2 | semidirect |
| 6. #23752418 | C2 | semidirect |
| 7. #23752413 | C2 | semidirect |
| 8. #23752408 | C2 | semidirect |
| 9. #23752376 | C2 | semidirect |
| 10. #23752359 | C2 | semidirect |
| 11. #431×C151 | C2 | semidirect |
| 144. C151 | #3212 | semidirect |
| 156. #431 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| #23752746 | 2 |
| #23752596 | 2 |
| #23752567 | 2 |
| #23752423 | 2 |
| #23752418 | 2 |
| #23752413 | 2 |
| #23752408 | 2 |
| #23752376 | 2 |
| #23752359 | 2 |
| #431×C151 | 2 |
| #3212 | 151 |