Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23752935 | C2 | semidirect |
| 3. #23752559 | C2 | semidirect |
| 4. #23752539 | C2 | semidirect |
| 5. #23752497 | C2 | semidirect |
| 6. #23752444 | C2 | semidirect |
| 7. #23752412 | C2 | semidirect |
| 8. #23752373 | C2 | semidirect |
| 9. C8×D604 | C2 | semidirect |
| 10. #23752207 | C2 | semidirect |
| 11. C4×Q16×C151 | C2 | semidirect |
| 127. C151 | #3304 | semidirect |
| 137. C4×Q16 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752935 | 2 |
| #23752884 | 2 |
| #23752559 | 2 |
| #23752539 | 2 |
| #23752497 | 2 |
| #23752444 | 2 |
| #23752412 | 2 |
| #23752373 | 2 |
| C8×D604 | 2 |
| #23752207 | 2 |
| C4×Q16×C151 | 2 |
| #3304 | 151 |