Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#14558989 | C2 | semidirect |
| 2. C2×#18012747 | C2 | semidirect |
| 3. #23752781 | C2 | semidirect |
| 4. #23752779 | C2 | semidirect |
| 5. #23752464 | C2 | semidirect |
| 6. #23752447 | C2 | semidirect |
| 7. #23752248 | C2 | semidirect |
| 8. #23752218 | C2 | semidirect |
| 9. #418×C151 | C2 | semidirect |
| 16. C2×#14558987 | C22 | semidirect |
| 18. C2×C8×D151 | C22 | semidirect |
| 23. #18012714 | C22 | semidirect |
| 24. #18012710 | C22 | semidirect |
| 28. #18012672 | C22 | semidirect |
| 29. #18012670 | C22 | semidirect |
| 30. #18012661 | C22 | semidirect |
| 34. #102×C151 | C22 | semidirect |
| 51. C2×C151⋊C8 | D4 | semidirect |
| 125. C151 | #3058 | semidirect |
| 135. #418 | D151 | semidirect |
| 160. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558989 | 2 |
| C2×#18012747 | 2 |
| #23752781 | 2 |
| #23752779 | 2 |
| #23752464 | 2 |
| #23752447 | 2 |
| #23752248 | 2 |
| #23752218 | 2 |
| #418×C151 | 2 |
| #3058 | 151 |