Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
544 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 128 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. C2×#91164 | C2 | semidirect |
| 3. #11746782 | C2 | semidirect |
| 4. C3×C22⋊#674 | C2 | semidirect |
| 5. #11746547 | C2 | semidirect |
| 15. C2×C3⋊#674 | C22 | semidirect |
| 16. C2×C3×#674 | C22 | semidirect |
| 22. C22⋊#674 | D3 | semidirect |
| 59. C2×#674 | C2×D3 | semidirect |
| 65. C22×D15 | C16 | semidirect |
| 124. C22×C3×C5 | C2×C16 | semidirect |
| 131. C2×D15 | C2×C16 | semidirect |
| 198. D15 | C22⋊C16 | semidirect |
| 224. C22×C5 | D3×C16 | semidirect |
| 259. C3×C5 | C2×C22⋊C16 | semidirect |
| 262. C22×C3 | D5⋊C16 | semidirect |
| 311. C5 | D3×C22⋊C16 | semidirect |
| 321. C22 | #91164 | semidirect |
| 328. C3 | D5⋊(C22⋊C16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6648 | 2 |
| C2×#91164 | 2 |
| #11746782 | 2 |
| C3×C22⋊#674 | 2 |
| #11746547 | 2 |
| D5⋊(C22⋊C16) | 3 |
| D3×C22⋊C16 | 5 |