Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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×#18012765 | C2 | semidirect |
| 2. C2×#18012761 | C2 | semidirect |
| 3. #23752779 | C2 | semidirect |
| 4. #23752600 | C2 | semidirect |
| 5. #23752595 | C2 | semidirect |
| 6. #23752587 | C2 | semidirect |
| 7. #23752167 | C2 | semidirect |
| 8. C22×D8×C151 | C2 | semidirect |
| 12. C2×Dic604 | C22 | semidirect |
| 13. C2×#14558993 | C22 | semidirect |
| 14. C2×#14558992 | C22 | semidirect |
| 15. C2×D1208 | C22 | semidirect |
| 16. C2×#14558989 | C22 | semidirect |
| 18. #18012735 | C22 | semidirect |
| 19. #18012726 | C22 | semidirect |
| 23. #18012649 | C22 | semidirect |
| 24. C8×Dic151 | C22 | semidirect |
| 42. #14558988 | D4 | semidirect |
| 56. C2×C8×C151 | D4 | semidirect |
| 101. C151 | #3155 | semidirect |
| 105. C22×D8 | D151 | semidirect |
| 154. 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×#18012765 | 2 |
| C2×#18012761 | 2 |
| #23752779 | 2 |
| #23752600 | 2 |
| #23752595 | 2 |
| #23752587 | 2 |
| #23752167 | 2 |
| C22×D8×C151 | 2 |
| #3155 | 151 |