Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012770 | C2 | semidirect |
| 2. C2×#18012765 | C2 | semidirect |
| 3. C2×#18012761 | C2 | semidirect |
| 4. #23752786 | C2 | semidirect |
| 5. #23752779 | C2 | semidirect |
| 6. #23752603 | C2 | semidirect |
| 7. #23752598 | C2 | semidirect |
| 8. #23752593 | C2 | semidirect |
| 9. #23752583 | C2 | semidirect |
| 10. #23752167 | C2 | semidirect |
| 11. C22×SD16×C151 | C2 | semidirect |
| 17. C2×Dic604 | C22 | semidirect |
| 18. C2×#14558994 | C22 | semidirect |
| 19. C2×#14558993 | C22 | semidirect |
| 20. C2×#14558993 | C22 | semidirect |
| 22. C2×#14558991 | C22 | semidirect |
| 23. C2×D1208 | C22 | semidirect |
| 26. #18012737 | C22 | semidirect |
| 28. #18012728 | C22 | semidirect |
| 35. #18012649 | C22 | semidirect |
| 36. C8×Dic151 | C22 | semidirect |
| 64. #14558988 | D4 | semidirect |
| 85. C2×C8×C151 | D4 | semidirect |
| 148. C151 | #3154 | semidirect |
| 153. C22×SD16 | D151 | semidirect |
| 228. C2×C8 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012770 | 2 |
| C2×#18012765 | 2 |
| C2×#18012761 | 2 |
| #23752786 | 2 |
| #23752779 | 2 |
| #23752603 | 2 |
| #23752598 | 2 |
| #23752593 | 2 |
| #23752583 | 2 |
| #23752167 | 2 |
| C22×SD16×C151 | 2 |
| #3154 | 151 |