Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 2. #23752550 | C2 | semidirect |
| 3. #23752509 | C2 | semidirect |
| 4. #23752414 | C2 | semidirect |
| 6. #23752310 | C2 | semidirect |
| 7. C4×#14558991 | C2 | semidirect |
| 8. #23752273 | C2 | semidirect |
| 9. #541×C151 | C2 | semidirect |
| 18. #18012672 | C22 | semidirect |
| 19. #18012670 | C22 | semidirect |
| 20. C4⋊(C151⋊C8) | C22 | semidirect |
| 21. #18012663 | C22 | semidirect |
| 22. #18012663 | C22 | semidirect |
| 26. #18012650 | C22 | semidirect |
| 27. C4×C151⋊C8 | C22 | semidirect |
| 28. C4⋊Q8×C151 | C22 | semidirect |
| 31. #125×C151 | C22 | semidirect |
| 33. C4×Q8×C151 | C22 | semidirect |
| 102. C151 | #3123 | semidirect |
| 104. #541 | D151 | semidirect |
| 116. C4⋊Q8 | C2×D151 | semidirect |
| 119. #125 | C2×D151 | semidirect |
| 121. C4×Q8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752686 | 2 |
| #23752550 | 2 |
| #23752509 | 2 |
| #23752414 | 2 |
| #23752362 | 2 |
| #23752310 | 2 |
| C4×#14558991 | 2 |
| #23752273 | 2 |
| #541×C151 | 2 |
| #3123 | 151 |