Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752824 | C2 | semidirect |
| 3. #23752614 | C2 | semidirect |
| 4. #23752585 | C2 | semidirect |
| 5. #23752581 | C2 | semidirect |
| 6. #23752577 | C2 | semidirect |
| 7. #23752458 | C2 | semidirect |
| 8. #23752441 | C2 | semidirect |
| 9. #23752314 | C2 | semidirect |
| 10. C4×#14558993 | C2 | semidirect |
| 11. #405×C151 | C2 | semidirect |
| 108. C151 | #3174 | semidirect |
| 120. #405 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752824 | 2 |
| #23752817 | 2 |
| #23752614 | 2 |
| #23752585 | 2 |
| #23752581 | 2 |
| #23752577 | 2 |
| #23752458 | 2 |
| #23752441 | 2 |
| #23752314 | 2 |
| C4×#14558993 | 2 |
| #405×C151 | 2 |
| #3174 | 151 |