Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #23752840 | C2 | semidirect |
| 3. #23752514 | C2 | semidirect |
| 4. #23752510 | C2 | semidirect |
| 5. #23752500 | C2 | semidirect |
| 6. #23752490 | C2 | semidirect |
| 7. #23752254 | C2 | semidirect |
| 8. #23752248 | C2 | semidirect |
| 9. #23752240 | C2 | semidirect |
| 14. #18012738 | C22 | semidirect |
| 16. #18012730 | C22 | semidirect |
| 26. #18012673 | C22 | semidirect |
| 27. #18012672 | C22 | semidirect |
| 28. #18012672 | C22 | semidirect |
| 29. #18012671 | C22 | semidirect |
| 30. #18012670 | C22 | semidirect |
| 31. #18012670 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. Dic151⋊C8 | C22 | semidirect |
| 66. 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 |
| #23752687 | 2 |
| #23752514 | 2 |
| #23752510 | 2 |
| #23752500 | 2 |
| #23752490 | 2 |
| #23752254 | 2 |
| #23752248 | 2 |
| #23752240 | 2 |
| C2×#18012660 | 2 |
| #418×C151 | 2 |
| #3081 | 151 |