Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752840 | C2 | semidirect |
| 3. #23752575 | C2 | semidirect |
| 4. #23752573 | C2 | semidirect |
| 5. #23752568 | C2 | semidirect |
| 6. #23752557 | C2 | semidirect |
| 7. #23752216 | C2 | semidirect |
| 8. #23752213 | C2 | semidirect |
| 9. C2×#18012661 | C2 | semidirect |
| 10. #23752167 | C2 | semidirect |
| 11. #416×C151 | C2 | semidirect |
| 15. #18012738 | C22 | semidirect |
| 18. #18012730 | C22 | semidirect |
| 26. #18012663 | C22 | semidirect |
| 29. #18012660 | C22 | semidirect |
| 32. #18012649 | C22 | semidirect |
| 33. C8×Dic151 | C22 | semidirect |
| 37. #103×C151 | C22 | semidirect |
| 38. #103×C151 | C22 | semidirect |
| 39. #102×C151 | C22 | semidirect |
| 40. #102×C151 | C22 | semidirect |
| 135. C151 | #3136 | semidirect |
| 145. #416 | D151 | semidirect |
| 166. #103 | C2×D151 | semidirect |
| 167. #103 | C2×D151 | semidirect |
| 173. #102 | C2×D151 | semidirect |
| 174. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752840 | 2 |
| #23752776 | 2 |
| #23752575 | 2 |
| #23752573 | 2 |
| #23752568 | 2 |
| #23752557 | 2 |
| #23752216 | 2 |
| #23752213 | 2 |
| C2×#18012661 | 2 |
| #23752167 | 2 |
| #416×C151 | 2 |
| #3136 | 151 |