Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23752746 | C2 | semidirect |
| 2. C2×#18012727 | C2 | semidirect |
| 3. #23752596 | C2 | semidirect |
| 4. #23752567 | C2 | semidirect |
| 5. #23752435 | C2 | semidirect |
| 6. #23752428 | C2 | semidirect |
| 7. #23752370 | C2 | semidirect |
| 8. #23752365 | C2 | semidirect |
| 9. #23752353 | C2 | semidirect |
| 11. #431×C151 | C2 | semidirect |
| 14. C2×Dic604 | C22 | semidirect |
| 16. C2×#14558993 | C22 | semidirect |
| 19. #18012731 | C22 | semidirect |
| 24. #18012727 | C22 | semidirect |
| 28. C4×Dic302 | C22 | semidirect |
| 29. C4×D604 | C22 | semidirect |
| 34. #18012664 | C22 | semidirect |
| 35. #18012664 | C22 | semidirect |
| 39. C4⋊C8×C151 | C22 | semidirect |
| 42. C4×C8×C151 | C22 | semidirect |
| 143. C151 | #3211 | semidirect |
| 155. #431 | D151 | semidirect |
| 179. C4⋊C8 | C2×D151 | semidirect |
| 186. C4×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752746 | 2 |
| C2×#18012727 | 2 |
| #23752596 | 2 |
| #23752567 | 2 |
| #23752435 | 2 |
| #23752428 | 2 |
| #23752370 | 2 |
| #23752365 | 2 |
| #23752353 | 2 |
| #23752348 | 2 |
| #431×C151 | 2 |
| #3211 | 151 |