Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×#91112 | C2 | semidirect |
| 2. C5×Dic3×Q16 | C2 | semidirect |
| 3. C2×C3×#3960 | C2 | semidirect |
| 5. Dic3⋊#672 | C2 | semidirect |
| 6. #11745896 | C2 | semidirect |
| 7. #11745891 | C2 | semidirect |
| 25. C2×#3960 | D3 | semidirect |
| 36. C3×C5×Q16 | D4 | semidirect |
| 51. Dic3×Q16 | D5 | semidirect |
| 108. C5×Q16 | #67 | semidirect |
| 141. C5×Dic3 | SD32 | semidirect |
| 148. C3×Q16 | D20 | semidirect |
| 235. Q16 | #1202 | semidirect |
| 249. C3×C5 | #2207 | semidirect |
| 262. Dic3 | #3960 | semidirect |
| 291. C5 | #71475 | semidirect |
| 305. C3 | #10601707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91112 | 2 |
| C5×Dic3×Q16 | 2 |
| C2×C3×#3960 | 2 |
| #11748005 | 2 |
| Dic3⋊#672 | 2 |
| #11745896 | 2 |
| #11745891 | 2 |
| #10601707 | 3 |
| #71475 | 5 |