Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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. #23753027 | C2 | semidirect |
| 2. #23753026 | C2 | semidirect |
| 3. #23752590 | C2 | semidirect |
| 4. #23752487 | C2 | semidirect |
| 5. #23752485 | C2 | semidirect |
| 6. #23752484 | C2 | semidirect |
| 7. #23752395 | C2 | semidirect |
| 8. #23752393 | C2 | semidirect |
| 9. #23752329 | C2 | semidirect |
| 10. #23752327 | C2 | semidirect |
| 11. #578×C151 | C2 | semidirect |
| 146. C151 | #3293 | semidirect |
| 150. #578 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753027 | 2 |
| #23753026 | 2 |
| #23752590 | 2 |
| #23752487 | 2 |
| #23752485 | 2 |
| #23752484 | 2 |
| #23752395 | 2 |
| #23752393 | 2 |
| #23752329 | 2 |
| #23752327 | 2 |
| #578×C151 | 2 |
| #3293 | 151 |