Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 616 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 |
|---|---|---|
| 2. #11750795 | C2 | semidirect |
| 3. #11747062 | C2 | semidirect |
| 4. #11746964 | C2 | semidirect |
| 5. C5×#4459 | C2 | semidirect |
| 6. C3×#64679 | C2 | semidirect |
| 7. #11745854 | C2 | semidirect |
| 12. #91758 | C22 | semidirect |
| 19. C3×C4×C5×C8 | C22 | semidirect |
| 21. C5×C4⋊(C3⋊C8) | C22 | semidirect |
| 22. C3×C4⋊#168 | C22 | semidirect |
| 33. #64679 | D3 | semidirect |
| 67. #4459 | D5 | semidirect |
| 79. C4×C5×C8 | C2×D3 | semidirect |
| 84. C4⋊#168 | C2×D3 | semidirect |
| 105. C5×D12 | SD16 | semidirect |
| 129. C3×C4×C8 | C2×D5 | semidirect |
| 134. C4⋊(C3⋊C8) | C2×D5 | semidirect |
| 263. C4×C8 | D3×D5 | semidirect |
| 294. D12 | #677 | semidirect |
| 348. C3×C5 | #1639 | semidirect |
| 412. C5 | #68196 | semidirect |
| 432. C3 | #10598975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D12×D20 | 2 |
| #11750795 | 2 |
| #11747062 | 2 |
| #11746964 | 2 |
| C5×#4459 | 2 |
| C3×#64679 | 2 |
| #11745854 | 2 |
| #10598975 | 3 |
| #68196 | 5 |