Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
384 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 131 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. #11746752 | C2 | semidirect |
| 5. #11746750 | C2 | semidirect |
| 29. C3×C5×D8 | C8 | semidirect |
| 53. C3×C5×D4 | C2×C8 | semidirect |
| 63. C3×C5×C8 | C2×C8 | semidirect |
| 81. C5×D8 | C3⋊C8 | semidirect |
| 103. C3×D8 | #170 | semidirect |
| 115. C5×D4 | C2×C3⋊C8 | semidirect |
| 125. C5×C8 | C2×C3⋊C8 | semidirect |
| 143. C3×D4 | C2×#170 | semidirect |
| 151. C3×C8 | C2×#170 | semidirect |
| 166. D8 | C3⋊#170 | semidirect |
| 176. C3×C5 | #1580 | semidirect |
| 192. D4 | C2×C3⋊#170 | semidirect |
| 203. C8 | C2×C3⋊#170 | semidirect |
| 208. C5 | #70878 | semidirect |
| 218. C3 | #10604792 | 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 |
| #11746752 | 2 |
| #11746750 | 2 |
| #10604792 | 3 |
| #70878 | 5 |