Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. #23752765 | C2 | semidirect |
| 3. #23752579 | C2 | semidirect |
| 4. #23752575 | C2 | semidirect |
| 5. #23752573 | C2 | semidirect |
| 6. #23752570 | C2 | semidirect |
| 7. #23752209 | C2 | semidirect |
| 8. #23752208 | C2 | semidirect |
| 9. #23752206 | C2 | semidirect |
| 10. C2×#18012649 | C2 | semidirect |
| 11. #416×C151 | C2 | semidirect |
| 125. C151 | #3135 | semidirect |
| 136. #416 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752765 | 2 |
| #23752758 | 2 |
| #23752579 | 2 |
| #23752575 | 2 |
| #23752573 | 2 |
| #23752570 | 2 |
| #23752209 | 2 |
| #23752208 | 2 |
| #23752206 | 2 |
| C2×#18012649 | 2 |
| #416×C151 | 2 |
| #3135 | 151 |