Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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. #23752843 | C2 | semidirect |
| 3. #23752515 | C2 | semidirect |
| 4. #23752511 | C2 | semidirect |
| 5. #23752501 | C2 | semidirect |
| 6. #23752491 | C2 | semidirect |
| 7. #23752248 | C2 | semidirect |
| 8. #23752240 | C2 | semidirect |
| 11. #428×C151 | C2 | semidirect |
| 15. #18012738 | C22 | semidirect |
| 17. #18012730 | C22 | semidirect |
| 26. #18012672 | C22 | semidirect |
| 27. #18012672 | C22 | semidirect |
| 28. #18012670 | C22 | semidirect |
| 29. #18012670 | C22 | semidirect |
| 30. Dic151⋊C8 | C22 | semidirect |
| 31. Dic151⋊C8 | C22 | semidirect |
| 39. #107×C151 | C22 | semidirect |
| 40. #106×C151 | C22 | semidirect |
| 45. C2×D604 | Q8 | semidirect |
| 124. C151 | #3081 | semidirect |
| 132. #428 | D151 | semidirect |
| 156. #107 | C2×D151 | semidirect |
| 159. #106 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752843 | 2 |
| #23752686 | 2 |
| #23752515 | 2 |
| #23752511 | 2 |
| #23752501 | 2 |
| #23752491 | 2 |
| #23752248 | 2 |
| #23752240 | 2 |
| #23752218 | 2 |
| C2×#18012659 | 2 |
| #428×C151 | 2 |
| #3081 | 151 |