Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23752760 | C2 | semidirect |
| 2. C4×#14559005 | C2 | semidirect |
| 3. #23752534 | C2 | semidirect |
| 4. #23752497 | C2 | semidirect |
| 5. #23752493 | C2 | semidirect |
| 6. #23752404 | C2 | semidirect |
| 7. #23752356 | C2 | semidirect |
| 8. #23752321 | C2 | semidirect |
| 9. #23752313 | C2 | semidirect |
| 10. #23752268 | C2 | semidirect |
| 11. #460×C151 | C2 | semidirect |
| 88. D604 | #41 | semidirect |
| 106. Q8×C151 | #41 | semidirect |
| 144. C151 | #3115 | semidirect |
| 151. #460 | D151 | semidirect |
| 233. Q8 | #14559003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752760 | 2 |
| C4×#14559005 | 2 |
| #23752534 | 2 |
| #23752497 | 2 |
| #23752493 | 2 |
| #23752404 | 2 |
| #23752356 | 2 |
| #23752321 | 2 |
| #23752313 | 2 |
| #23752268 | 2 |
| #460×C151 | 2 |
| #3115 | 151 |