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×#18012762 | C2 | semidirect |
| 2. #23752763 | C2 | semidirect |
| 3. C4×#14559005 | C2 | semidirect |
| 4. #23752436 | C2 | semidirect |
| 5. #23752430 | C2 | semidirect |
| 6. #23752414 | C2 | semidirect |
| 7. #23752412 | C2 | semidirect |
| 8. #23752408 | C2 | semidirect |
| 9. C4⋊C8×D151 | C2 | semidirect |
| 10. #23752207 | C2 | semidirect |
| 11. #462×C151 | C2 | semidirect |
| 47. #14559005 | D4 | semidirect |
| 137. C4×C151 | #135 | semidirect |
| 150. C151 | #3035 | semidirect |
| 157. #462 | D151 | semidirect |
| 292. C4 | #18012762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012762 | 2 |
| #23752763 | 2 |
| C4×#14559005 | 2 |
| #23752436 | 2 |
| #23752430 | 2 |
| #23752414 | 2 |
| #23752412 | 2 |
| #23752408 | 2 |
| C4⋊C8×D151 | 2 |
| #23752207 | 2 |
| #462×C151 | 2 |
| #3035 | 151 |