Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 2. #11747009 | C2 | semidirect |
| 3. C5×#4458 | C2 | semidirect |
| 4. C3×C8×#168 | C2 | semidirect |
| 5. #11745839 | C2 | semidirect |
| 22. C8×#168 | D3 | semidirect |
| 40. #4458 | D5 | semidirect |
| 62. C3×C5×C8 | M16 | semidirect |
| 65. C3×#168 | D8 | semidirect |
| 129. C5×C8 | ΓL(1,𝔽25) | semidirect |
| 132. #168 | D24 | semidirect |
| 160. C3×C8 | #676 | semidirect |
| 185. C3×C5 | #1589 | semidirect |
| 214. C8 | #6651 | semidirect |
| 219. C5 | #68052 | semidirect |
| 230. C3 | #10599356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D120 | 2 |
| #11747009 | 2 |
| C5×#4458 | 2 |
| C3×C8×#168 | 2 |
| #11745839 | 2 |
| #10599356 | 3 |
| #68052 | 5 |