Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18012767 | C2 | semidirect |
| 2. C2×#18012759 | C2 | semidirect |
| 3. #23752776 | C2 | semidirect |
| 4. #23752693 | C2 | semidirect |
| 5. #23752437 | C2 | semidirect |
| 6. #23752430 | C2 | semidirect |
| 7. #23752411 | C2 | semidirect |
| 8. #23752406 | C2 | semidirect |
| 9. #23752240 | C2 | semidirect |
| 10. C2×#18012659 | C2 | semidirect |
| 11. #417×C151 | C2 | semidirect |
| 16. C2×#14558994 | C22 | semidirect |
| 18. C2×#14558992 | C22 | semidirect |
| 19. C2×#14558991 | C22 | semidirect |
| 21. C2×#14558989 | C22 | semidirect |
| 28. #18012704 | C22 | semidirect |
| 29. #18012701 | C22 | semidirect |
| 34. Dic151⋊C8 | C22 | semidirect |
| 35. Dic151⋊C8 | C22 | semidirect |
| 41. #103×C151 | C22 | semidirect |
| 42. #102×C151 | C22 | semidirect |
| 45. #14559004 | D4 | semidirect |
| 154. C151 | #3045 | semidirect |
| 165. #417 | D151 | semidirect |
| 194. #103 | C2×D151 | semidirect |
| 197. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012767 | 2 |
| C2×#18012759 | 2 |
| #23752776 | 2 |
| #23752693 | 2 |
| #23752437 | 2 |
| #23752430 | 2 |
| #23752411 | 2 |
| #23752406 | 2 |
| #23752240 | 2 |
| C2×#18012659 | 2 |
| #417×C151 | 2 |
| #3045 | 151 |