Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 87 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×D8×D15 | C2 | semidirect |
| 2. C2×C3×C5×D16 | C2 | semidirect |
| 3. #11751258 | C2 | semidirect |
| 4. C2×#91110 | C2 | semidirect |
| 5. #11746383 | C2 | semidirect |
| 6. #11746330 | C2 | semidirect |
| 7. #11746328 | C2 | semidirect |
| 11. C2×C3×C5×D8 | C22 | semidirect |
| 19. C2×C3×C5×C16 | C22 | semidirect |
| 22. #91102 | C22 | semidirect |
| 23. C2×C3⋊#672 | C22 | semidirect |
| 26. C2×C5×D16 | D3 | semidirect |
| 44. C3×C5×D8 | D4 | semidirect |
| 51. D120 | D4 | semidirect |
| 57. C2×C3×D16 | D5 | semidirect |
| 65. C2×C5×D8 | C2×D3 | semidirect |
| 73. C2×C5×C16 | C2×D3 | semidirect |
| 104. C2×C3×D8 | C2×D5 | semidirect |
| 112. C2×C3×C16 | C2×D5 | semidirect |
| 129. C5×D8 | #67 | semidirect |
| 143. C2×D16 | D15 | semidirect |
| 161. C2×D15 | D16 | semidirect |
| 178. C3×D8 | C22⋊D5 | semidirect |
| 219. C2×D8 | C2×D15 | semidirect |
| 225. C2×C16 | C2×D15 | semidirect |
| 291. D8 | #1220 | semidirect |
| 300. C3×C5 | #2184 | semidirect |
| 356. C5 | #71467 | semidirect |
| 375. C3 | #10602260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D15 | 2 |
| C2×C3×C5×D16 | 2 |
| #11751258 | 2 |
| C2×#91110 | 2 |
| #11746383 | 2 |
| #11746330 | 2 |
| #11746328 | 2 |
| #10602260 | 3 |
| #71467 | 5 |