Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 2. #23752550 | C2 | semidirect |
| 3. #23752536 | C2 | semidirect |
| 4. #23752460 | C2 | semidirect |
| 5. #23752443 | C2 | semidirect |
| 6. #23752362 | C2 | semidirect |
| 7. #23752351 | C2 | semidirect |
| 8. #23752179 | C2 | semidirect |
| 9. #536×C151 | C2 | semidirect |
| 13. C2×#14558988 | C22 | semidirect |
| 14. C22×C151⋊C8 | C22 | semidirect |
| 22. #18012672 | C22 | semidirect |
| 23. #18012670 | C22 | semidirect |
| 24. #18012663 | C22 | semidirect |
| 25. #18012663 | C22 | semidirect |
| 29. C22⋊(C151⋊C8) | C22 | semidirect |
| 31. C22×Q8×C151 | C22 | semidirect |
| 37. C22⋊Q8×C151 | C22 | semidirect |
| 38. #117×C151 | C22 | semidirect |
| 137. C151 | #3200 | semidirect |
| 139. #536 | D151 | semidirect |
| 149. C22×Q8 | C2×D151 | semidirect |
| 162. C22⋊Q8 | C2×D151 | semidirect |
| 168. #117 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752776 | 2 |
| #23752550 | 2 |
| #23752536 | 2 |
| #23752460 | 2 |
| #23752443 | 2 |
| #23752362 | 2 |
| #23752351 | 2 |
| #23752179 | 2 |
| #536×C151 | 2 |
| #3200 | 151 |