Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×#66091 | C2 | semidirect |
| 2. C2×C3×C5×D16 | C2 | semidirect |
| 3. C3×#65449 | C2 | semidirect |
| 4. C3×#65436 | C2 | semidirect |
| 5. C3×#64783 | C2 | semidirect |
| 6. C3×#64730 | C2 | semidirect |
| 7. C3×#64728 | C2 | semidirect |
| 8. #10602264 | C3 | direct (N × H) |
| 11. C2×C3×C5×D8 | C22 | semidirect |
| 20. C2×C3×C5×C16 | C22 | semidirect |
| 24. C3×#3951 | C22 | semidirect |
| 25. C3×#3944 | C22 | semidirect |
| 27. #66091 | C2×C3 | semidirect |
| 28. C2×C5×D16 | C2×C3 | semidirect |
| 29. #65449 | C2×C3 | semidirect |
| 30. #65436 | C2×C3 | semidirect |
| 31. #64783 | C2×C3 | semidirect |
| 32. #64730 | C2×C3 | semidirect |
| 33. #64728 | C2×C3 | semidirect |
| 63. C2×C3×D16 | D5 | semidirect |
| 70. C2×C5×D8 | C22×C3 | semidirect |
| 79. C2×C5×C16 | C22×C3 | semidirect |
| 83. #3951 | C22×C3 | semidirect |
| 84. #3944 | C22×C3 | semidirect |
| 117. C2×C3×D8 | C2×D5 | semidirect |
| 123. C2×C3×C16 | C2×D5 | semidirect |
| 155. C2×D16 | C3×D5 | semidirect |
| 230. C2×D8 | C2×C3×D5 | semidirect |
| 236. C2×C16 | C2×C3×D5 | semidirect |
| 307. C3×C5 | #2192 | semidirect |
| 355. C5 | C3×#2192 | semidirect |
| 368. C3 | #10602264 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66091 | 2 |
| C2×C3×C5×D16 | 2 |
| C3×#65449 | 2 |
| C3×#65436 | 2 |
| C3×#64783 | 2 |
| C3×#64730 | 2 |
| C3×#64728 | 2 |
| #10602264 | 3 |
| C3×#2192 | 5 |