Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
662 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 162 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×Dic15 | C2 | semidirect |
| 3. C22×C3×C5×Dic3 | C2 | semidirect |
| 4. #10623813 | C2 | direct (N × H) |
| 10. C22×C3⋊D15 | C4 | semidirect |
| 13. C2×C3×Dic15 | C22 | semidirect |
| 15. C2×C3×C5×Dic3 | C22 | semidirect |
| 21. C22×Dic15 | D3 | semidirect |
| 22. C22×C5×Dic3 | D3 | semidirect |
| 33. C2×C3⋊D15 | C2×C4 | semidirect |
| 39. C22×C3×Dic3 | D5 | semidirect |
| 59. C2×Dic15 | C2×D3 | semidirect |
| 61. C2×C5×Dic3 | C2×D3 | semidirect |
| 66. C2×C32×C5 | C22⋊C4 | semidirect |
| 83. C2×C3×Dic3 | C2×D5 | semidirect |
| 118. C22×Dic3 | D15 | semidirect |
| 121. C32×C5 | C2×C22⋊C4 | semidirect |
| 146. C2×C3×C5 | (C2×D3)⋊C4 | semidirect |
| 147. C2×C3×C5 | (C2×D3)⋊C4 | semidirect |
| 179. C2×Dic3 | C2×D15 | semidirect |
| 190. C2×C32 | #685 | semidirect |
| 200. C3×C5 | C2×(C2×D3)⋊C4 | semidirect |
| 201. C3×C5 | C2×(C2×D3)⋊C4 | semidirect |
| 230. C2×C5 | #3722 | semidirect |
| 235. C32 | C2×#685 | semidirect |
| 249. C2×C3 | #6667 | semidirect |
| 250. C2×C3 | #6714 | semidirect |
| 260. C5 | C2×#3722 | semidirect |
| 272. C3 | C2×#6667 | semidirect |
| 273. C3 | C2×#6714 | semidirect |
| 275. C2 | #10623813 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊D15 | 2 |
| C22×C3×Dic15 | 2 |
| C22×C3×C5×Dic3 | 2 |
| #10623813 | 2 |
| C2×#6714 | 3 |
| C2×#6667 | 3 |
| C2×#3722 | 5 |