Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. Q8×Dic302 | C2 | semidirect |
| 3. #23752559 | C2 | semidirect |
| 4. #23752557 | C2 | semidirect |
| 5. #23752502 | C2 | semidirect |
| 6. #23752501 | C2 | semidirect |
| 7. #23752412 | C2 | semidirect |
| 8. #23752410 | C2 | semidirect |
| 9. C8×Dic302 | C2 | semidirect |
| 10. #23752297 | C2 | semidirect |
| 11. C4×SD16×C151 | C2 | semidirect |
| 77. Dic302 | SD16 | semidirect |
| 91. Q8×C151 | #41 | semidirect |
| 125. C151 | #3362 | semidirect |
| 137. C4×SD16 | D151 | semidirect |
| 206. Q8 | #14559004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic302 | 2 |
| #23752883 | 2 |
| #23752559 | 2 |
| #23752557 | 2 |
| #23752502 | 2 |
| #23752501 | 2 |
| #23752412 | 2 |
| #23752410 | 2 |
| C8×Dic302 | 2 |
| #23752297 | 2 |
| C4×SD16×C151 | 2 |
| #3362 | 151 |