Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 100 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. C5×#5570 | C2 | semidirect |
| 5. C3×Q8⋊#168 | C2 | semidirect |
| 6. #11745858 | C2 | semidirect |
| 7. #11745843 | C2 | semidirect |
| 33. Q8⋊#168 | D3 | semidirect |
| 58. #5570 | D5 | semidirect |
| 85. C3×C5×Q8 | SD16 | semidirect |
| 198. C5×Q8 | #204 | semidirect |
| 238. C3×Q8 | #688 | semidirect |
| 297. C3×C5 | #1626 | semidirect |
| 322. Q8 | #6660 | semidirect |
| 343. C5 | #68252 | semidirect |
| 358. C3 | #10602728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5570 | 2 |
| #11751128 | 2 |
| #11747078 | 2 |
| #11746912 | 2 |
| C3×Q8⋊#168 | 2 |
| #11745858 | 2 |
| #11745843 | 2 |
| #10602728 | 3 |
| #68252 | 5 |