Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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. C2×#18012746 | C2 | semidirect |
| 2. #23752334 | C2 | semidirect |
| 3. #23752329 | C2 | semidirect |
| 4. #23752261 | C2 | semidirect |
| 5. #23752229 | C2 | semidirect |
| 6. #23752170 | C2 | semidirect |
| 10. #18012746 | C22 | semidirect |
| 11. #18012746 | C22 | semidirect |
| 17. #18012675 | C22 | semidirect |
| 18. #18012666 | C22 | semidirect |
| 19. #18012649 | C22 | semidirect |
| 20. C8×Dic151 | C22 | semidirect |
| 22. #137×C151 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C151 | C4 | semidirect |
| 89. C151 | #2955 | semidirect |
| 99. #137 | Dic151 | semidirect |
| 100. AGL(1,ℤ/8) | Dic151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012746 | 2 |
| #23752334 | 2 |
| #23752329 | 2 |
| #23752261 | 2 |
| #23752229 | 2 |
| #23752170 | 2 |
| #575×C151 | 2 |
| #2955 | 151 |