Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
294 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10624226 | C2 | semidirect |
| 2. #10624224 | C2 | semidirect |
| 3. C5×#3745 | C2 | semidirect |
| 4. C3×#6706 | C2 | semidirect |
| 5. C3×#6705 | C2 | semidirect |
| 6. #10623824 | C2 | semidirect |
| 7. #10623821 | C2 | semidirect |
| 12. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 15. C3×Dic30 | C22 | semidirect |
| 19. C32×C5×C8 | C22 | semidirect |
| 20. C3×C3⋊#168 | C22 | semidirect |
| 26. #6706 | D3 | semidirect |
| 27. #6705 | D3 | semidirect |
| 48. #3745 | D5 | semidirect |
| 57. Dic30 | C2×D3 | semidirect |
| 74. C3×C5×C8 | C2×D3 | semidirect |
| 75. C3×C5×C8 | C2×D3 | semidirect |
| 76. C3⋊#168 | C2×D3 | semidirect |
| 94. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 101. C32×C8 | C2×D5 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 147. C5×C8 | D32 | semidirect |
| 193. C3×C8 | D3×D5 | semidirect |
| 194. C3×C8 | D3×D5 | semidirect |
| 217. C3×C5 | #908 | semidirect |
| 218. C3×C5 | #914 | semidirect |
| 243. C32 | #4057 | semidirect |
| 254. C8 | (C3⋊D3)⋊D5 | semidirect |
| 268. C5 | #63794 | semidirect |
| 278. C3 | #91250 | semidirect |
| 279. C3 | #91257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624226 | 2 |
| #10624224 | 2 |
| C5×#3745 | 2 |
| C3×#6706 | 2 |
| C3×#6705 | 2 |
| #10623824 | 2 |
| #10623821 | 2 |
| #91257 | 3 |
| #91250 | 3 |
| #63794 | 5 |