Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#18012760 | C2 | semidirect |
| 2. #23752760 | C2 | semidirect |
| 3. C4×#14559005 | C2 | semidirect |
| 4. #23752432 | C2 | semidirect |
| 5. #23752426 | C2 | semidirect |
| 6. #23752422 | C2 | semidirect |
| 7. #23752418 | C2 | semidirect |
| 8. #23752404 | C2 | semidirect |
| 9. C4⋊C8×D151 | C2 | semidirect |
| 10. #23752205 | C2 | semidirect |
| 11. #460×C151 | C2 | semidirect |
| 45. #14559005 | D4 | semidirect |
| 136. C4×C151 | #135 | semidirect |
| 150. C151 | #3035 | semidirect |
| 159. #460 | D151 | semidirect |
| 292. C4 | #18012760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012760 | 2 |
| #23752760 | 2 |
| C4×#14559005 | 2 |
| #23752432 | 2 |
| #23752426 | 2 |
| #23752422 | 2 |
| #23752418 | 2 |
| #23752404 | 2 |
| C4⋊C8×D151 | 2 |
| #23752205 | 2 |
| #460×C151 | 2 |
| #3035 | 151 |