Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
384 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 55. C3×C5×C8 | Q16 | semidirect |
| 57. C3⋊#168 | Q16 | semidirect |
| 107. C5×C8 | #216 | semidirect |
| 129. C3×C8 | #689 | semidirect |
| 149. C3×C5 | #1713 | semidirect |
| 168. C8 | #6661 | semidirect |
| 172. C5 | #71362 | semidirect |
| 179. C3 | #10602155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4682 | 2 |
| C3×#64971 | 2 |
| #11747103 | 2 |
| #11746962 | 2 |
| C8×C3⋊#168 | 2 |
| #10602155 | 3 |
| #71362 | 5 |