Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 98 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×Dic30 | C2 | semidirect |
| 3. #11747086 | C2 | semidirect |
| 4. #11746906 | C2 | semidirect |
| 5. C3×D4⋊#168 | C2 | semidirect |
| 6. #11745860 | C2 | semidirect |
| 7. #11745845 | C2 | semidirect |
| 31. D4⋊#168 | D3 | semidirect |
| 88. C3×C5×D4 | SD16 | semidirect |
| 103. Dic30 | D8 | semidirect |
| 212. C5×D4 | #204 | semidirect |
| 256. C3×D4 | #687 | semidirect |
| 322. C3×C5 | #1627 | semidirect |
| 357. D4 | #6659 | semidirect |
| 376. C5 | #68187 | semidirect |
| 393. C3 | #10601807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic30 | 2 |
| C5×#5015 | 2 |
| #11747086 | 2 |
| #11746906 | 2 |
| C3×D4⋊#168 | 2 |
| #11745860 | 2 |
| #11745845 | 2 |
| #10601807 | 3 |
| #68187 | 5 |