Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23752748 | C2 | semidirect |
| 2. C2×D4×Dic151 | C2 | semidirect |
| 3. #23752540 | C2 | semidirect |
| 4. #23752526 | C2 | semidirect |
| 5. #23752510 | C2 | semidirect |
| 6. #23752429 | C2 | semidirect |
| 8. #23752321 | C2 | semidirect |
| 9. #23752313 | C2 | semidirect |
| 10. #23752266 | C2 | semidirect |
| 11. #450×C151 | C2 | semidirect |
| 15. #18012730 | C22 | semidirect |
| 16. #18012728 | C22 | semidirect |
| 19. Q8×Dic151 | C22 | semidirect |
| 24. #18012701 | C22 | semidirect |
| 30. #18012673 | C22 | semidirect |
| 31. #18012670 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012663 | C22 | semidirect |
| 34. #18012661 | C22 | semidirect |
| 37. #18012649 | C22 | semidirect |
| 140. C151 | #3114 | semidirect |
| 148. #450 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752748 | 2 |
| C2×D4×Dic151 | 2 |
| #23752540 | 2 |
| #23752526 | 2 |
| #23752510 | 2 |
| #23752429 | 2 |
| #23752346 | 2 |
| #23752321 | 2 |
| #23752313 | 2 |
| #23752266 | 2 |
| #450×C151 | 2 |
| #3114 | 151 |