Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×C3×C5×Q16 | C2 | semidirect |
| 2. C2×#91112 | C2 | semidirect |
| 4. #11746385 | C2 | semidirect |
| 5. #11746370 | C2 | semidirect |
| 19. C22×C5×Q16 | D3 | semidirect |
| 34. C3×C5×Q16 | D4 | semidirect |
| 42. C22×C3×Q16 | D5 | semidirect |
| 97. C5×Q16 | #67 | semidirect |
| 105. C22×Q16 | D15 | semidirect |
| 112. C22×C3×C5 | SD32 | semidirect |
| 132. C3×Q16 | C22⋊D5 | semidirect |
| 192. C22×C5 | #828 | semidirect |
| 212. Q16 | #1220 | semidirect |
| 220. C3×C5 | #2185 | semidirect |
| 223. C22×C3 | #3960 | semidirect |
| 260. C5 | #72063 | semidirect |
| 266. C22 | #91112 | semidirect |
| 273. C3 | #10602856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q16 | 2 |
| C2×#91112 | 2 |
| #11751216 | 2 |
| #11746385 | 2 |
| #11746370 | 2 |
| #10602856 | 3 |
| #72063 | 5 |