Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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 |
|---|---|---|
| 1. C22×#14558989 | C2 | semidirect |
| 2. C2×#18012746 | C2 | semidirect |
| 3. #23752776 | C2 | semidirect |
| 4. #23752463 | C2 | semidirect |
| 5. #23752446 | C2 | semidirect |
| 6. #23752248 | C2 | semidirect |
| 7. #23752217 | C2 | semidirect |
| 8. #23752216 | C2 | semidirect |
| 9. #535×C151 | C2 | semidirect |
| 16. C2×#14558988 | C22 | semidirect |
| 18. C22×C151⋊C8 | C22 | semidirect |
| 21. #18012713 | C22 | semidirect |
| 24. #18012672 | C22 | semidirect |
| 25. #18012670 | C22 | semidirect |
| 26. #18012660 | C22 | semidirect |
| 27. #18012659 | C22 | semidirect |
| 32. #121×C151 | C22 | semidirect |
| 46. C2×C151⋊C8 | D4 | semidirect |
| 125. C151 | #3058 | semidirect |
| 130. #535 | D151 | semidirect |
| 152. #121 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558989 | 2 |
| C2×#18012746 | 2 |
| #23752776 | 2 |
| #23752463 | 2 |
| #23752446 | 2 |
| #23752248 | 2 |
| #23752217 | 2 |
| #23752216 | 2 |
| #535×C151 | 2 |
| #3058 | 151 |