Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
266 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 74 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. C4⋊(C3⋊Dic15) | C2 | semidirect |
| 2. C3×#6712 | C2 | semidirect |
| 4. #10623815 | C2 | semidirect |
| 7. Dic3×Dic15 | C2 | semidirect |
| 25. #6712 | D3 | semidirect |
| 127. C32×C5 | #126 | semidirect |
| 196. C3×C5 | #879 | semidirect |
| 197. C3×C5 | #898 | semidirect |
| 226. C32 | #4025 | semidirect |
| 245. C5 | #63861 | semidirect |
| 257. C3 | #91342 | semidirect |
| 258. C3 | #91768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊(C3⋊Dic15) | 2 |
| C3×#6712 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| #10623815 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| Dic3×Dic15 | 2 |
| #91768 | 3 |
| #91342 | 3 |
| #63861 | 5 |