Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic302 | C2 | semidirect |
| 3. #23752563 | C2 | semidirect |
| 4. #23752543 | C2 | semidirect |
| 5. #23752498 | C2 | semidirect |
| 6. #23752441 | C2 | semidirect |
| 7. #23752418 | C2 | semidirect |
| 8. #23752353 | C2 | semidirect |
| 9. C4×#14558993 | C2 | semidirect |
| 10. C2×#18012664 | C2 | semidirect |
| 11. C8×D4×C151 | C2 | semidirect |
| 83. Dic302 | #41 | semidirect |
| 96. D4×C151 | SD16 | semidirect |
| 128. C151 | #3298 | semidirect |
| 139. C8×D4 | D151 | semidirect |
| 217. D4 | #14558993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic302 | 2 |
| #23752866 | 2 |
| #23752563 | 2 |
| #23752543 | 2 |
| #23752498 | 2 |
| #23752441 | 2 |
| #23752418 | 2 |
| #23752353 | 2 |
| C4×#14558993 | 2 |
| C2×#18012664 | 2 |
| C8×D4×C151 | 2 |
| #3298 | 151 |