Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
192 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 4. #10598807 | C3 | direct (N × H) |
| 19. C3×C5×Q16 | C8 | semidirect |
| 59. C5×Q16 | C3×C8 | semidirect |
| 79. C3×Q16 | #170 | semidirect |
| 129. Q16 | C3×#170 | semidirect |
| 138. C3×C5 | #1334 | semidirect |
| 163. C5 | C3×#1334 | semidirect |
| 171. C3 | #10598807 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q16×Dic5 | 2 |
| C3×#64886 | 2 |
| C3×#64881 | 2 |
| #10598807 | 3 |
| C3×#1334 | 5 |