Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 108 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. C3×#65761 | C2 | semidirect |
| 3. C3×#65745 | C2 | semidirect |
| 4. C3×#64934 | C2 | semidirect |
| 5. #10604940 | C3 | direct (N × H) |
| 6. C22×C3×C5×D4 | C4 | semidirect |
| 10. C3×#4099 | C4 | semidirect |
| 16. C3×#4072 | C4 | semidirect |
| 23. #65761 | C2×C3 | semidirect |
| 24. #65745 | C2×C3 | semidirect |
| 25. #64934 | C2×C3 | semidirect |
| 57. C22×C5×D4 | C3×C4 | semidirect |
| 61. #4099 | C3×C4 | semidirect |
| 67. #4072 | C3×C4 | semidirect |
| 102. C22×C3×D4 | AGL(1,𝔽5) | semidirect |
| 221. C22×D4 | C3×AGL(1,𝔽5) | semidirect |
| 314. C3×C5 | #2122 | semidirect |
| 373. C5 | C3×#2122 | semidirect |
| 392. C3 | #10604940 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66139 | 2 |
| C3×#65761 | 2 |
| C3×#65745 | 2 |
| C3×#64934 | 2 |
| #10604940 | 3 |
| C3×#2122 | 5 |