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 |
| 2. #23752564 | C2 | semidirect |
| 3. #23752542 | C2 | semidirect |
| 4. #23752494 | C2 | semidirect |
| 5. #23752439 | C2 | semidirect |
| 6. #23752417 | C2 | semidirect |
| 7. #23752350 | C2 | semidirect |
| 8. C4×#14558992 | C2 | semidirect |
| 9. D4×C151⋊C8 | C2 | semidirect |
| 10. C2×#18012662 | C2 | semidirect |
| 81. Dic302 | #41 | semidirect |
| 95. D4×C151 | SD16 | semidirect |
| 128. C151 | #3298 | semidirect |
| 217. D4 | #14558992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic302 | 2 |
| #23752564 | 2 |
| #23752542 | 2 |
| #23752494 | 2 |
| #23752439 | 2 |
| #23752417 | 2 |
| #23752350 | 2 |
| C4×#14558992 | 2 |
| D4×C151⋊C8 | 2 |
| C2×#18012662 | 2 |
| #547×C151 | 2 |
| #3298 | 151 |