Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14558991 | C2 | semidirect |
| 3. #23752686 | C2 | semidirect |
| 4. #23752424 | C2 | semidirect |
| 5. #23752414 | C2 | semidirect |
| 6. #23752239 | C2 | semidirect |
| 7. #23752221 | C2 | semidirect |
| 8. #23752208 | C2 | semidirect |
| 9. #536×C151 | C2 | semidirect |
| 22. C4⋊(C151⋊C8) | C22 | semidirect |
| 23. #18012663 | C22 | semidirect |
| 24. #18012663 | C22 | semidirect |
| 25. #18012660 | C22 | semidirect |
| 28. C4⋊Q8×C151 | C22 | semidirect |
| 29. #124×C151 | C22 | semidirect |
| 116. C151 | #3042 | semidirect |
| 120. #536 | D151 | semidirect |
| 137. C4⋊Q8 | C2×D151 | semidirect |
| 138. #124 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012764 | 2 |
| C22×#14558991 | 2 |
| #23752686 | 2 |
| #23752424 | 2 |
| #23752414 | 2 |
| #23752239 | 2 |
| #23752221 | 2 |
| #23752208 | 2 |
| #536×C151 | 2 |
| #3042 | 151 |