Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 122 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. C22×C3×C5×Q16 | C2 | semidirect |
| 2. C2×C3×#3960 | C2 | semidirect |
| 4. C3×#64784 | C2 | semidirect |
| 5. C3×C22⋊#672 | C2 | semidirect |
| 6. #10602856 | C3 | direct (N × H) |
| 19. C22×C5×Q16 | C2×C3 | semidirect |
| 20. C2×#3960 | C2×C3 | semidirect |
| 22. #64784 | C2×C3 | semidirect |
| 23. C22⋊#672 | C2×C3 | semidirect |
| 34. C3×C5×Q16 | D4 | semidirect |
| 42. C22×C3×Q16 | D5 | semidirect |
| 97. C5×Q16 | C3×D4 | semidirect |
| 105. C22×Q16 | C3×D5 | semidirect |
| 112. C22×C3×C5 | SD32 | semidirect |
| 132. C3×Q16 | C22⋊D5 | semidirect |
| 192. C22×C5 | C3×SD32 | semidirect |
| 212. Q16 | C3×C22⋊D5 | semidirect |
| 220. C3×C5 | #2185 | semidirect |
| 226. C22×C3 | #3960 | semidirect |
| 260. C5 | C3×#2185 | semidirect |
| 266. C22 | C3×#3960 | semidirect |
| 273. C3 | #10602856 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q16 | 2 |
| C2×C3×#3960 | 2 |
| C3×#65404 | 2 |
| C3×#64784 | 2 |
| C3×C22⋊#672 | 2 |
| #10602856 | 3 |
| C3×#2185 | 5 |