Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 76. C3×C5×Q8 | Q16 | semidirect |
| 162. C5×Q8 | #216 | semidirect |
| 198. C3×Q8 | #689 | semidirect |
| 241. C3×C5 | #1670 | semidirect |
| 260. Q8 | #6718 | semidirect |
| 276. C5 | #71117 | semidirect |
| 287. C3 | #10601910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#475 | 2 |
| #11751193 | 2 |
| Q8×C3⋊#168 | 2 |
| #11751121 | 2 |
| #11746368 | 2 |
| #11746307 | 2 |
| #11746300 | 2 |
| #10601910 | 3 |
| #71117 | 5 |