Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18012772 | C2 | semidirect |
| 3. C2×#18012727 | C2 | semidirect |
| 4. C4×#14559004 | C2 | semidirect |
| 5. #23752435 | C2 | semidirect |
| 6. #23752428 | C2 | semidirect |
| 7. #23752222 | C2 | semidirect |
| 8. #23752218 | C2 | semidirect |
| 9. #423×C151 | C2 | semidirect |
| 15. C2×Dic604 | C22 | semidirect |
| 17. C2×#14558993 | C22 | semidirect |
| 22. C4×Dic302 | C22 | semidirect |
| 23. C4×D604 | C22 | semidirect |
| 29. #18012664 | C22 | semidirect |
| 34. C4⋊C8×C151 | C22 | semidirect |
| 125. C151 | #3040 | semidirect |
| 133. #423 | D151 | semidirect |
| 158. C4⋊C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012772 | 2 |
| C2×#18012767 | 2 |
| C2×#18012727 | 2 |
| C4×#14559004 | 2 |
| #23752435 | 2 |
| #23752428 | 2 |
| #23752222 | 2 |
| #23752218 | 2 |
| #423×C151 | 2 |
| #3040 | 151 |