Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23752840 | C2 | semidirect |
| 2. #23752512 | C2 | semidirect |
| 3. #23752512 | C2 | semidirect |
| 4. #23752502 | C2 | semidirect |
| 5. #23752492 | C2 | semidirect |
| 6. #23752255 | C2 | semidirect |
| 7. #23752248 | C2 | semidirect |
| 8. #23752239 | C2 | semidirect |
| 14. #18012739 | C22 | semidirect |
| 16. #18012731 | C22 | semidirect |
| 21. #18012672 | C22 | semidirect |
| 22. #18012672 | C22 | semidirect |
| 23. #18012672 | C22 | semidirect |
| 24. #18012670 | C22 | semidirect |
| 25. #18012670 | C22 | semidirect |
| 26. #18012670 | C22 | semidirect |
| 27. C4⋊(C151⋊C8) | C22 | semidirect |
| 28. C4⋊(C151⋊C8) | C22 | semidirect |
| 60. C2×D4×C151 | Q8 | semidirect |
| 124. C151 | #3081 | semidirect |
| 170. C2×D4 | Dic302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752840 | 2 |
| #23752512 | 2 |
| #23752502 | 2 |
| #23752492 | 2 |
| #23752255 | 2 |
| #23752248 | 2 |
| #23752239 | 2 |
| #23752217 | 2 |
| C2×#18012660 | 2 |
| #518×C151 | 2 |
| #3081 | 151 |