Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23752757 | C2 | semidirect |
| 2. C2×D4×Dic151 | C2 | semidirect |
| 3. #23752531 | C2 | semidirect |
| 4. #23752528 | C2 | semidirect |
| 5. #23752500 | C2 | semidirect |
| 6. #23752405 | C2 | semidirect |
| 7. #23752346 | C2 | semidirect |
| 8. #23752324 | C2 | semidirect |
| 9. #23752321 | C2 | semidirect |
| 10. #23752266 | C2 | semidirect |
| 11. #447×C151 | C2 | semidirect |
| 15. #18012738 | C22 | semidirect |
| 16. #18012735 | C22 | semidirect |
| 24. D4×Dic151 | C22 | semidirect |
| 25. #18012701 | C22 | semidirect |
| 30. #18012671 | C22 | semidirect |
| 31. #18012670 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012661 | C22 | semidirect |
| 35. #18012660 | C22 | semidirect |
| 37. #18012649 | C22 | semidirect |
| 113. D4×C151 | #41 | semidirect |
| 149. C151 | #3109 | semidirect |
| 158. #447 | D151 | semidirect |
| 249. D4 | #14559003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752757 | 2 |
| C2×D4×Dic151 | 2 |
| #23752531 | 2 |
| #23752528 | 2 |
| #23752500 | 2 |
| #23752405 | 2 |
| #23752346 | 2 |
| #23752324 | 2 |
| #23752321 | 2 |
| #23752266 | 2 |
| #447×C151 | 2 |
| #3109 | 151 |