Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. C2×#18012719 | C2 | semidirect |
| 3. #23752555 | C2 | semidirect |
| 4. #23752530 | C2 | semidirect |
| 5. #23752469 | C2 | semidirect |
| 6. #23752459 | C2 | semidirect |
| 7. #23752377 | C2 | semidirect |
| 8. #23752367 | C2 | semidirect |
| 9. #23752353 | C2 | semidirect |
| 10. #23752174 | C2 | semidirect |
| 11. #484×C151 | C2 | semidirect |
| 15. C2×#14558994 | C22 | semidirect |
| 16. C2×#14558993 | C22 | semidirect |
| 32. #18012670 | C22 | semidirect |
| 33. #18012664 | C22 | semidirect |
| 34. #18012662 | C22 | semidirect |
| 35. #18012659 | C22 | semidirect |
| 40. #107×C151 | C22 | semidirect |
| 41. #103×C151 | C22 | semidirect |
| 149. C151 | #3196 | semidirect |
| 154. #484 | D151 | semidirect |
| 184. #107 | C2×D151 | semidirect |
| 188. #103 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752725 | 2 |
| C2×#18012719 | 2 |
| #23752555 | 2 |
| #23752530 | 2 |
| #23752469 | 2 |
| #23752459 | 2 |
| #23752377 | 2 |
| #23752367 | 2 |
| #23752353 | 2 |
| #23752174 | 2 |
| #484×C151 | 2 |
| #3196 | 151 |