Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
384 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 146 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 |
|---|---|---|
| 6. #10602155 | C3 | direct (N × H) |
| 55. C3×C5×C8 | Q16 | semidirect |
| 57. C3×#168 | Q16 | semidirect |
| 107. C5×C8 | C3×Q16 | semidirect |
| 109. #168 | C3×Q16 | semidirect |
| 131. C3×C8 | #689 | semidirect |
| 149. C3×C5 | #1713 | semidirect |
| 168. C8 | C3×#689 | semidirect |
| 172. C5 | C3×#1713 | semidirect |
| 179. C3 | #10602155 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| C3×#65381 | 2 |
| C3×#65367 | 2 |
| C3×#64971 | 2 |
| C3×C8×#168 | 2 |
| #10602155 | 3 |
| C3×#1713 | 5 |