Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 104 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. #11751120 | C2 | semidirect |
| 3. #11746890 | C2 | semidirect |
| 4. #11746889 | C2 | semidirect |
| 5. C5×D4⋊(C3⋊C8) | C2 | semidirect |
| 6. #11745852 | C2 | semidirect |
| 7. #11745835 | C2 | semidirect |
| 13. #91758 | C22 | semidirect |
| 20. C4⋊(C3⋊#168) | C22 | semidirect |
| 21. C5×C4⋊(C3⋊C8) | C22 | semidirect |
| 22. C4×C5×C3⋊C8 | C22 | semidirect |
| 67. D4⋊(C3⋊C8) | D5 | semidirect |
| 112. C3×D20 | SD16 | semidirect |
| 133. C4⋊(C3⋊C8) | C2×D5 | semidirect |
| 134. C4×C3⋊C8 | C2×D5 | semidirect |
| 239. D20 | #214 | semidirect |
| 348. C3×C5 | #1639 | semidirect |
| 412. C5 | #71908 | semidirect |
| 432. C3 | #10598989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×D20 | 2 |
| #11751120 | 2 |
| #11746890 | 2 |
| #11746889 | 2 |
| C5×D4⋊(C3⋊C8) | 2 |
| #11745852 | 2 |
| #11745835 | 2 |
| #10598989 | 3 |
| #71908 | 5 |