Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23753026 | C2 | semidirect |
| 2. #23753025 | C2 | semidirect |
| 3. #23752655 | C2 | semidirect |
| 4. #23752654 | C2 | semidirect |
| 5. #23752651 | C2 | semidirect |
| 6. #23752643 | C2 | semidirect |
| 7. #23752642 | C2 | semidirect |
| 8. C2×#18012685 | C2 | semidirect |
| 9. Q32×D151 | C2 | semidirect |
| 10. #23752630 | C2 | semidirect |
| 11. #510×C151 | C2 | semidirect |
| 123. C151 | #3417 | semidirect |
| 130. #510 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753026 | 2 |
| #23753025 | 2 |
| #23752655 | 2 |
| #23752654 | 2 |
| #23752651 | 2 |
| #23752643 | 2 |
| #23752642 | 2 |
| C2×#18012685 | 2 |
| Q32×D151 | 2 |
| #23752630 | 2 |
| #510×C151 | 2 |
| #3417 | 151 |