Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 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. #23752769 | C2 | semidirect |
| 2. #23752622 | C2 | semidirect |
| 3. #23752607 | C2 | semidirect |
| 4. #23752582 | C2 | semidirect |
| 5. #23752571 | C2 | semidirect |
| 6. #23752468 | C2 | semidirect |
| 8. C4×#14558994 | C2 | semidirect |
| 9. C4×#14558992 | C2 | semidirect |
| 10. C4×#14558988 | C2 | semidirect |
| 129. C151 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752769 | 2 |
| #23752622 | 2 |
| #23752607 | 2 |
| #23752582 | 2 |
| #23752571 | 2 |
| #23752468 | 2 |
| #23752456 | 2 |
| C4×#14558994 | 2 |
| C4×#14558992 | 2 |
| C4×#14558988 | 2 |
| #529×C151 | 2 |
| #3172 | 151 |