Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
788 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 4. C22×C4×C5×Q8 | C3 | semidirect |
| 5. C5×Q8×A4 | C4 | direct (N × H) |
| 10. C4×Q8×A4 | C5 | direct (N × H) |
| 22. C4×C5×A4 | Q8 | direct (N × H) |
| 31. C22×C5×Q8 | C3×C4 | semidirect |
| 41. C4×C5×Q8 | A4 | direct (N × H) |
| 49. C22×C4×Q8 | C3×C5 | semidirect |
| 57. Q8×A4 | C4×C5 | direct (N × H) |
| 81. C22×C4×C5 | C3×Q8 | semidirect |
| 99. C5×A4 | C4×Q8 | direct (N × H) |
| 107. C4×A4 | C5×Q8 | direct (N × H) |
| 119. C5×Q8 | C4×A4 | direct (N × H) |
| 141. C22×Q8 | C3×C4×C5 | semidirect |
| 151. C4×Q8 | C5×A4 | direct (N × H) |
| 179. C22×C5 | C3×C4×Q8 | semidirect |
| 186. C4×C5 | Q8×A4 | direct (N × H) |
| 206. C22×C4 | C3×C5×Q8 | semidirect |
| 218. A4 | C4×C5×Q8 | direct (N × H) |
| 238. Q8 | C4×C5×A4 | direct (N × H) |
| 260. C5 | C4×Q8×A4 | direct (N × H) |
| 271. C22 | C3×C4×C5×Q8 | semidirect |
| 278. C4 | C5×Q8×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×A4 | 2 |
| C5×A4×C4⋊C4 | 2 |
| C42×C5×A4 | 2 |
| C22×C4×C5×Q8 | 3 |
| C3×C4×C5×Q8 | 4 |
| C4×Q8×A4 | 5 |