Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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×#18012701 | C2 | semidirect |
| 3. #23752525 | C2 | semidirect |
| 4. #23752511 | C2 | semidirect |
| 5. #23752430 | C2 | semidirect |
| 6. #23752362 | C2 | semidirect |
| 8. #23752323 | C2 | semidirect |
| 9. #23752315 | C2 | semidirect |
| 10. #23752266 | C2 | semidirect |
| 11. #483×C151 | C2 | semidirect |
| 17. #18012730 | C22 | semidirect |
| 18. #18012728 | C22 | semidirect |
| 21. Q8×Dic151 | C22 | semidirect |
| 26. #18012701 | C22 | semidirect |
| 31. #18012672 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 35. #18012659 | C22 | semidirect |
| 37. #18012649 | C22 | semidirect |
| 40. #106×C151 | C22 | semidirect |
| 41. #103×C151 | C22 | semidirect |
| 140. C151 | #3114 | semidirect |
| 144. #483 | D151 | semidirect |
| 175. #106 | C2×D151 | semidirect |
| 177. #103 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752748 | 2 |
| C2×#18012701 | 2 |
| #23752525 | 2 |
| #23752511 | 2 |
| #23752430 | 2 |
| #23752362 | 2 |
| #23752348 | 2 |
| #23752323 | 2 |
| #23752315 | 2 |
| #23752266 | 2 |
| #483×C151 | 2 |
| #3114 | 151 |