Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 90 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. C3×Q8×#170 | C2 | semidirect |
| 4. #11746801 | C2 | semidirect |
| 5. #11746514 | C2 | semidirect |
| 7. #11746487 | C2 | semidirect |
| 25. Q8×#170 | D3 | semidirect |
| 75. C3×C5×Q8 | M16 | semidirect |
| 165. C5×Q8 | ΓL(1,𝔽25) | semidirect |
| 204. C3×Q8 | #700 | semidirect |
| 252. C3×C5 | #1588 | semidirect |
| 271. Q8 | #6740 | semidirect |
| 293. C5 | #70936 | semidirect |
| 306. C3 | #10603978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×#170 | 2 |
| #11751914 | 2 |
| #11749221 | 2 |
| #11746801 | 2 |
| #11746514 | 2 |
| #11746490 | 2 |
| #11746487 | 2 |
| #10603978 | 3 |
| #70936 | 5 |