Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #23752978 | C2 | semidirect |
| 3. #23752335 | C2 | semidirect |
| 4. #23752330 | C2 | semidirect |
| 5. #23752261 | C2 | semidirect |
| 6. C2×#18012667 | C2 | semidirect |
| 7. C4×M16×C151 | C2 | semidirect |
| 9. #18012772 | C4 | semidirect |
| 10. #18012767 | C4 | semidirect |
| 13. #18012745 | C22 | semidirect |
| 16. #18012675 | C22 | semidirect |
| 17. #18012667 | C22 | semidirect |
| 18. #18012667 | C22 | semidirect |
| 22. #97×C151 | C22 | semidirect |
| 23. C4×C8×C151 | C22 | semidirect |
| 32. Dic604 | C2×C4 | semidirect |
| 33. #14558993 | C2×C4 | semidirect |
| 34. D1208 | C2×C4 | semidirect |
| 85. C151 | #2956 | semidirect |
| 93. C4×M16 | D151 | semidirect |
| 108. #97 | C2×D151 | semidirect |
| 109. C4×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753012 | 2 |
| #23752978 | 2 |
| #23752335 | 2 |
| #23752330 | 2 |
| #23752261 | 2 |
| C2×#18012667 | 2 |
| C4×M16×C151 | 2 |
| #2956 | 151 |