Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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×C8×D151 | C2 | semidirect |
| 2. #23752719 | C2 | semidirect |
| 3. #23752450 | C2 | semidirect |
| 4. #23752445 | C2 | semidirect |
| 5. #23752438 | C2 | semidirect |
| 6. #23752250 | C2 | semidirect |
| 7. #23752208 | C2 | semidirect |
| 8. C2×#135×C151 | C2 | semidirect |
| 20. #18012673 | C22 | semidirect |
| 21. #18012671 | C22 | semidirect |
| 22. #18012663 | C22 | semidirect |
| 23. #18012660 | C22 | semidirect |
| 26. C2×Q16×C151 | C22 | semidirect |
| 27. C2×SD16×C151 | C22 | semidirect |
| 28. C2×D8×C151 | C22 | semidirect |
| 57. C2×C8×C151 | D4 | semidirect |
| 94. C2×D151 | #135 | semidirect |
| 106. C151 | #3050 | semidirect |
| 108. C2×#135 | D151 | semidirect |
| 119. C2×Q16 | C2×D151 | semidirect |
| 120. C2×SD16 | C2×D151 | semidirect |
| 121. C2×D8 | C2×D151 | semidirect |
| 158. 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×C8×D151 | 2 |
| #23752719 | 2 |
| #23752450 | 2 |
| #23752445 | 2 |
| #23752438 | 2 |
| #23752250 | 2 |
| #23752208 | 2 |
| C2×#135×C151 | 2 |
| #3050 | 151 |