Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23752765 | C2 | semidirect |
| 3. #23752575 | C2 | semidirect |
| 4. #23752557 | C2 | semidirect |
| 5. #23752218 | C2 | semidirect |
| 6. #23752217 | C2 | semidirect |
| 7. #23752216 | C2 | semidirect |
| 8. M16×Dic151 | C2 | semidirect |
| 9. #418×C151 | C2 | semidirect |
| 13. #18012738 | C22 | semidirect |
| 17. #18012730 | C22 | semidirect |
| 22. #18012661 | C22 | semidirect |
| 23. #18012660 | C22 | semidirect |
| 24. #18012659 | C22 | semidirect |
| 25. #18012649 | C22 | semidirect |
| 26. C8×Dic151 | C22 | semidirect |
| 30. #102×C151 | C22 | semidirect |
| 111. C151 | #3138 | semidirect |
| 120. #418 | D151 | semidirect |
| 140. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752765 | 2 |
| C2×#18012735 | 2 |
| #23752575 | 2 |
| #23752557 | 2 |
| #23752218 | 2 |
| #23752217 | 2 |
| #23752216 | 2 |
| M16×Dic151 | 2 |
| #418×C151 | 2 |
| #3138 | 151 |