Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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×#18012728 | C2 | semidirect |
| 3. #23752597 | C2 | semidirect |
| 4. #23752568 | C2 | semidirect |
| 5. #23752436 | C2 | semidirect |
| 6. #23752430 | C2 | semidirect |
| 7. #23752362 | C2 | semidirect |
| 8. #23752351 | C2 | semidirect |
| 10. #23752262 | C2 | semidirect |
| 11. #451×C151 | C2 | semidirect |
| 14. C2×#14558991 | C22 | semidirect |
| 17. #18012730 | C22 | semidirect |
| 22. #18012728 | C22 | semidirect |
| 25. Q8×Dic151 | C22 | semidirect |
| 26. #18012701 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012663 | C22 | semidirect |
| 37. C8×Dic151 | C22 | semidirect |
| 39. C2×Q16×C151 | C22 | semidirect |
| 41. #103×C151 | C22 | semidirect |
| 143. C151 | #3211 | semidirect |
| 151. #451 | D151 | semidirect |
| 158. C2×Q16 | C2×D151 | semidirect |
| 181. #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×#18012728 | 2 |
| #23752597 | 2 |
| #23752568 | 2 |
| #23752436 | 2 |
| #23752430 | 2 |
| #23752362 | 2 |
| #23752351 | 2 |
| #23752348 | 2 |
| #23752262 | 2 |
| #451×C151 | 2 |
| #3211 | 151 |