Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 62 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. C3×D4×D15 | C2 | semidirect |
| 2. #10624200 | C2 | semidirect |
| 3. #10623910 | C2 | semidirect |
| 4. C3×C5×#213 | C2 | semidirect |
| 5. #10623803 | C2 | semidirect |
| 6. #10623798 | C2 | semidirect |
| 7. #10623795 | C2 | semidirect |
| 12. #67180 | C22 | semidirect |
| 16. C3×C5×D12 | C22 | semidirect |
| 19. C3⋊(C3⋊#168) | C22 | semidirect |
| 20. C3×C5×C3⋊C8 | C22 | semidirect |
| 23. D4×D15 | D3 | semidirect |
| 33. C5×#213 | D3 | semidirect |
| 49. C3×#213 | D5 | semidirect |
| 67. C5×D12 | C2×D3 | semidirect |
| 77. C5×C3⋊C8 | C2×D3 | semidirect |
| 97. C3×D12 | C2×D5 | semidirect |
| 102. C3×C3⋊C8 | C2×D5 | semidirect |
| 133. #213 | D15 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 184. D12 | C2×D15 | semidirect |
| 194. C3⋊C8 | C2×D15 | semidirect |
| 216. C3×C5 | #911 | semidirect |
| 217. C3×C5 | #932 | semidirect |
| 242. C32 | #4057 | semidirect |
| 266. C5 | #63932 | semidirect |
| 276. C3 | #91489 | semidirect |
| 277. C3 | #91800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×D15 | 2 |
| #10624200 | 2 |
| #10623910 | 2 |
| C3×C5×#213 | 2 |
| #10623803 | 2 |
| #10623798 | 2 |
| #10623795 | 2 |
| #91800 | 3 |
| #91489 | 3 |
| #63932 | 5 |