Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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. C2×#18012761 | C2 | semidirect |
| 2. C22×#14558987 | C2 | semidirect |
| 3. #23752724 | C2 | semidirect |
| 4. #23752471 | C2 | semidirect |
| 5. #23752466 | C2 | semidirect |
| 6. #23752459 | C2 | semidirect |
| 7. #23752206 | C2 | semidirect |
| 8. #427×C151 | C2 | semidirect |
| 12. C2×Dic604 | C22 | semidirect |
| 13. C2×#14558993 | C22 | semidirect |
| 14. C2×D1208 | C22 | semidirect |
| 24. #18012662 | C22 | semidirect |
| 25. #18012659 | C22 | semidirect |
| 28. #107×C151 | C22 | semidirect |
| 29. #106×C151 | C22 | semidirect |
| 54. C2×C8×C151 | D4 | semidirect |
| 105. C151 | #3054 | semidirect |
| 113. #427 | D151 | semidirect |
| 132. #107 | C2×D151 | semidirect |
| 133. #106 | C2×D151 | semidirect |
| 157. C2×C8 | D604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012761 | 2 |
| C22×#14558987 | 2 |
| #23752724 | 2 |
| #23752471 | 2 |
| #23752466 | 2 |
| #23752459 | 2 |
| #23752206 | 2 |
| #427×C151 | 2 |
| #3054 | 151 |