Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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. D4×C3⋊#170 | C2 | semidirect |
| 3. D4⋊(C3⋊#170) | C2 | semidirect |
| 4. #11746753 | C2 | semidirect |
| 5. C8×C3⋊#170 | C2 | semidirect |
| 30. C3×C5×D8 | C8 | semidirect |
| 54. C3×C5×D4 | C2×C8 | semidirect |
| 64. C3⋊#170 | D8 | direct (N × H) |
| 65. C3×C5×C8 | C2×C8 | semidirect |
| 84. C5×D8 | C3⋊C8 | semidirect |
| 107. C3×D8 | #170 | semidirect |
| 120. C5×D4 | C2×C3⋊C8 | semidirect |
| 131. C5×C8 | C2×C3⋊C8 | semidirect |
| 149. C3×D4 | C2×#170 | semidirect |
| 157. C3×C8 | C2×#170 | semidirect |
| 174. D8 | C3⋊#170 | direct (N × H) |
| 185. C3×C5 | C8×D8 | semidirect |
| 202. D4 | C2×C3⋊#170 | semidirect |
| 214. C8 | C2×C3⋊#170 | semidirect |
| 219. C5 | D8×C3⋊C8 | semidirect |
| 230. C3 | D8×#170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C3⋊#170 | 2 |
| C3×D8×Dic5 | 2 |
| D4⋊(C3⋊#170) | 2 |
| #11746753 | 2 |
| C8×C3⋊#170 | 2 |
| D8×#170 | 3 |
| D8×C3⋊C8 | 5 |