Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#18012768 | C2 | semidirect |
| 2. #23752877 | C2 | semidirect |
| 4. #23752591 | C2 | semidirect |
| 5. #23752469 | C2 | semidirect |
| 6. #23752423 | C2 | semidirect |
| 7. #23752371 | C2 | semidirect |
| 8. #23752369 | C2 | semidirect |
| 9. C4×#14558992 | C2 | semidirect |
| 10. #23752289 | C2 | semidirect |
| 11. #461×C151 | C2 | semidirect |
| 57. #14558992 | D4 | semidirect |
| 122. C4×C151 | #137 | semidirect |
| 134. C151 | #3276 | semidirect |
| 142. #461 | D151 | semidirect |
| 261. C4 | #18012768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012768 | 2 |
| #23752877 | 2 |
| #23752866 | 2 |
| #23752591 | 2 |
| #23752469 | 2 |
| #23752423 | 2 |
| #23752371 | 2 |
| #23752369 | 2 |
| C4×#14558992 | 2 |
| #23752289 | 2 |
| #461×C151 | 2 |
| #3276 | 151 |