Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23752834 | C2 | semidirect |
| 2. #23752616 | C2 | semidirect |
| 3. #23752597 | C2 | semidirect |
| 4. #23752573 | C2 | semidirect |
| 5. #23752461 | C2 | semidirect |
| 6. #23752450 | C2 | semidirect |
| 8. #23752310 | C2 | semidirect |
| 9. C4×D1208 | C2 | semidirect |
| 10. #23752166 | C2 | semidirect |
| 11. C4×Q16×C151 | C2 | semidirect |
| 117. C151 | #3175 | semidirect |
| 127. C4×Q16 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752834 | 2 |
| #23752616 | 2 |
| #23752597 | 2 |
| #23752573 | 2 |
| #23752461 | 2 |
| #23752450 | 2 |
| #23752449 | 2 |
| #23752310 | 2 |
| C4×D1208 | 2 |
| #23752166 | 2 |
| C4×Q16×C151 | 2 |
| #3175 | 151 |