Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#18012765 | C2 | semidirect |
| 2. #23752762 | C2 | semidirect |
| 3. #23752599 | C2 | semidirect |
| 4. #23752588 | C2 | semidirect |
| 5. #23752584 | C2 | semidirect |
| 6. C4×#14558988 | C2 | semidirect |
| 7. C2×#127×C151 | C2 | semidirect |
| 10. C2×#14558992 | C22 | semidirect |
| 11. C2×#14558989 | C22 | semidirect |
| 13. #18012739 | C22 | semidirect |
| 14. #18012736 | C22 | semidirect |
| 15. #18012727 | C22 | semidirect |
| 18. #18012650 | C22 | semidirect |
| 19. C4×C151⋊C8 | C22 | semidirect |
| 34. #14558988 | D4 | semidirect |
| 57. C151⋊C8 | C2×D4 | semidirect |
| 82. C4×C151 | AGL(1,ℤ/8) | semidirect |
| 90. C151 | #3151 | semidirect |
| 94. C2×#127 | D151 | semidirect |
| 174. C4 | #18012765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012765 | 2 |
| #23752762 | 2 |
| #23752599 | 2 |
| #23752588 | 2 |
| #23752584 | 2 |
| C4×#14558988 | 2 |
| C2×#127×C151 | 2 |
| #3151 | 151 |