Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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. C2×#18012764 | C2 | semidirect |
| 2. C22×D1208 | C2 | semidirect |
| 3. #23752776 | C2 | semidirect |
| 4. #23752598 | C2 | semidirect |
| 5. #23752597 | C2 | semidirect |
| 6. #23752587 | C2 | semidirect |
| 7. #23752167 | C2 | semidirect |
| 8. C2×#135×C151 | C2 | semidirect |
| 11. C2×#14558991 | C22 | semidirect |
| 15. C2×#14558989 | C22 | semidirect |
| 17. #18012735 | C22 | semidirect |
| 18. #18012728 | C22 | semidirect |
| 22. #18012649 | C22 | semidirect |
| 23. C8×Dic151 | C22 | semidirect |
| 26. C2×Q16×C151 | C22 | semidirect |
| 27. C2×SD16×C151 | C22 | semidirect |
| 28. C2×D8×C151 | C22 | semidirect |
| 40. #14558988 | D4 | semidirect |
| 56. C2×C8×C151 | D4 | semidirect |
| 101. C151 | #3155 | semidirect |
| 104. C2×#135 | D151 | semidirect |
| 115. C2×Q16 | C2×D151 | semidirect |
| 117. C2×SD16 | C2×D151 | semidirect |
| 122. C2×D8 | C2×D151 | semidirect |
| 154. C2×C8 | C22⋊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×D1208 | 2 |
| #23752776 | 2 |
| #23752598 | 2 |
| #23752597 | 2 |
| #23752587 | 2 |
| #23752167 | 2 |
| C2×#135×C151 | 2 |
| #3155 | 151 |