Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 2. C22×C3×C5×Dic3 | C2 | semidirect |
| 3. C2×#67149 | C2 | semidirect |
| 4. C3×#6719 | C2 | semidirect |
| 5. #10623815 | C2 | semidirect |
| 6. #10623813 | C2 | semidirect |
| 7. Dic3×Dic15 | C2 | semidirect |
| 12. #67184 | C4 | semidirect |
| 26. C22×C5×Dic3 | D3 | semidirect |
| 28. #6719 | D3 | semidirect |
| 38. C22×C32×C5 | C2×C4 | semidirect |
| 42. C2×C3⋊D15 | C2×C4 | semidirect |
| 43. C3⋊Dic15 | C2×C4 | semidirect |
| 47. C3×C5×Dic3 | D4 | semidirect |
| 50. C22×C3×Dic3 | D5 | semidirect |
| 112. C22×C3×C5 | C4×D3 | semidirect |
| 113. C22×C3×C5 | C4×D3 | semidirect |
| 135. C5×Dic3 | #67 | semidirect |
| 140. C22×Dic3 | D15 | semidirect |
| 151. C32×C5 | C4×D4 | semidirect |
| 164. C22×C32 | C4×D5 | semidirect |
| 173. C3×Dic3 | C22⋊D5 | semidirect |
| 216. C22×C5 | #624 | semidirect |
| 239. C3×C5 | #67⋊C4 | semidirect |
| 240. C3×C5 | C4×#67 | semidirect |
| 249. C22×C3 | #1200 | semidirect |
| 250. C22×C3 | C4×D15 | semidirect |
| 272. Dic3 | #1220 | semidirect |
| 278. C32 | C4×C22⋊D5 | semidirect |
| 304. C5 | #63952 | semidirect |
| 310. C22 | #67149 | semidirect |
| 318. C3 | #91556 | semidirect |
| 319. C3 | C4×#1220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67184 | 2 |
| C22×C3×C5×Dic3 | 2 |
| C2×#67149 | 2 |
| C3×#6719 | 2 |
| #10623815 | 2 |
| #10623813 | 2 |
| Dic3×Dic15 | 2 |
| C4×#1220 | 3 |
| #91556 | 3 |
| #63952 | 5 |