Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 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. C22×#14558993 | C2 | semidirect |
| 2. #23752783 | C2 | semidirect |
| 4. #23752458 | C2 | semidirect |
| 5. #23752441 | C2 | semidirect |
| 6. #23752250 | C2 | semidirect |
| 7. #23752222 | C2 | semidirect |
| 8. #23752218 | C2 | semidirect |
| 9. C2×#131×C151 | C2 | semidirect |
| 20. #18012718 | C22 | semidirect |
| 25. #18012673 | C22 | semidirect |
| 26. #18012671 | C22 | semidirect |
| 27. #18012664 | C22 | semidirect |
| 32. C2×M16×C151 | C22 | semidirect |
| 34. C22×C8×C151 | C22 | semidirect |
| 67. C2×C8×C151 | D4 | semidirect |
| 120. C151 | #3057 | semidirect |
| 123. C2×#131 | D151 | semidirect |
| 139. C2×M16 | C2×D151 | semidirect |
| 141. C22×C8 | C2×D151 | semidirect |
| 179. C2×C8 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558993 | 2 |
| #23752783 | 2 |
| #23752776 | 2 |
| #23752458 | 2 |
| #23752441 | 2 |
| #23752250 | 2 |
| #23752222 | 2 |
| #23752218 | 2 |
| C2×#131×C151 | 2 |
| #3057 | 151 |