Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 93 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. D8×Dic15 | C2 | semidirect |
| 3. #11750973 | C2 | semidirect |
| 4. C3×C5×#357 | C2 | semidirect |
| 5. #11746330 | C2 | semidirect |
| 6. C16×Dic15 | C2 | semidirect |
| 7. #11746310 | C2 | semidirect |
| 16. #91110 | C4 | semidirect |
| 25. C5×#357 | D3 | semidirect |
| 34. C3×C5×D8 | C2×C4 | semidirect |
| 43. D120 | C2×C4 | semidirect |
| 45. C3⋊#672 | C2×C4 | semidirect |
| 49. C3×#357 | D5 | semidirect |
| 99. C5×D8 | C4×D3 | semidirect |
| 116. #357 | D15 | semidirect |
| 130. Dic15 | D16 | semidirect |
| 136. C3×D8 | C4×D5 | semidirect |
| 217. D8 | C4×D15 | semidirect |
| 227. C3×C5 | C4×D16 | semidirect |
| 267. C5 | #69174 | semidirect |
| 281. C3 | #10599967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic15 | 2 |
| C2×#91110 | 2 |
| #11750973 | 2 |
| C3×C5×#357 | 2 |
| #11746330 | 2 |
| C16×Dic15 | 2 |
| #11746310 | 2 |
| #10599967 | 3 |
| #69174 | 5 |