Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18012759 | C2 | semidirect |
| 2. #23752883 | C2 | semidirect |
| 3. #23752588 | C2 | semidirect |
| 4. #23752446 | C2 | semidirect |
| 5. #23752412 | C2 | semidirect |
| 6. #23752409 | C2 | semidirect |
| 7. #23752357 | C2 | semidirect |
| 8. #23752355 | C2 | semidirect |
| 9. C4×#14558994 | C2 | semidirect |
| 10. D4×C151⋊C8 | C2 | semidirect |
| 11. #550×C151 | C2 | semidirect |
| 51. #14558994 | D4 | semidirect |
| 131. C4×C151 | #135 | semidirect |
| 142. C151 | #3287 | semidirect |
| 146. #550 | D151 | semidirect |
| 276. C4 | #18012759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012759 | 2 |
| #23752883 | 2 |
| #23752588 | 2 |
| #23752446 | 2 |
| #23752412 | 2 |
| #23752409 | 2 |
| #23752357 | 2 |
| #23752355 | 2 |
| C4×#14558994 | 2 |
| D4×C151⋊C8 | 2 |
| #550×C151 | 2 |
| #3287 | 151 |