Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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. C2×#18012718 | C2 | semidirect |
| 2. #23752553 | C2 | semidirect |
| 3. #23752540 | C2 | semidirect |
| 4. #23752523 | C2 | semidirect |
| 5. #23752451 | C2 | semidirect |
| 6. #23752439 | C2 | semidirect |
| 7. #23752374 | C2 | semidirect |
| 8. #23752367 | C2 | semidirect |
| 9. #23752350 | C2 | semidirect |
| 10. C2×C22⋊(C151⋊C8) | C2 | semidirect |
| 13. C2×#14558994 | C22 | semidirect |
| 14. C2×#14558992 | C22 | semidirect |
| 23. #18012672 | C22 | semidirect |
| 24. #18012670 | C22 | semidirect |
| 25. #18012663 | C22 | semidirect |
| 26. #18012662 | C22 | semidirect |
| 27. #18012662 | C22 | semidirect |
| 28. #18012660 | C22 | semidirect |
| 149. C151 | #3190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012718 | 2 |
| #23752553 | 2 |
| #23752540 | 2 |
| #23752523 | 2 |
| #23752451 | 2 |
| #23752439 | 2 |
| #23752374 | 2 |
| #23752367 | 2 |
| #23752350 | 2 |
| C2×C22⋊(C151⋊C8) | 2 |
| #525×C151 | 2 |
| #3190 | 151 |