Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#18012767 | C2 | semidirect |
| 2. C2×#18012764 | C2 | semidirect |
| 3. #23752758 | C2 | semidirect |
| 4. C2×#18012701 | C2 | semidirect |
| 5. #23752430 | C2 | semidirect |
| 6. #23752426 | C2 | semidirect |
| 7. #23752416 | C2 | semidirect |
| 8. #23752406 | C2 | semidirect |
| 9. #23752235 | C2 | semidirect |
| 10. #23752211 | C2 | semidirect |
| 11. #417×C151 | C2 | semidirect |
| 22. #18012737 | C22 | semidirect |
| 23. #18012735 | C22 | semidirect |
| 24. #18012728 | C22 | semidirect |
| 25. #18012726 | C22 | semidirect |
| 36. Dic151⋊C8 | C22 | semidirect |
| 37. Dic151⋊C8 | C22 | semidirect |
| 38. #18012662 | C22 | semidirect |
| 39. #18012659 | C22 | semidirect |
| 43. #103×C151 | C22 | semidirect |
| 44. #102×C151 | C22 | semidirect |
| 51. C2×D604 | D4 | semidirect |
| 158. Dic151 | AGL(1,ℤ/8) | semidirect |
| 166. C151 | #3036 | semidirect |
| 178. #417 | D151 | semidirect |
| 209. #103 | C2×D151 | semidirect |
| 211. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012767 | 2 |
| C2×#18012764 | 2 |
| #23752758 | 2 |
| C2×#18012701 | 2 |
| #23752430 | 2 |
| #23752426 | 2 |
| #23752416 | 2 |
| #23752406 | 2 |
| #23752235 | 2 |
| #23752211 | 2 |
| #417×C151 | 2 |
| #3036 | 151 |