Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 292 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. #10624227 | C2 | semidirect |
| 2. #10624220 | C2 | semidirect |
| 3. C5×#3743 | C2 | semidirect |
| 4. C3×D120 | C2 | semidirect |
| 5. C3×#6706 | C2 | semidirect |
| 6. #10623825 | C2 | semidirect |
| 7. #10623822 | C2 | semidirect |
| 14. C3×D60 | C22 | semidirect |
| 15. C3×Dic30 | C22 | semidirect |
| 19. C32×C5×C8 | C22 | semidirect |
| 20. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 26. D120 | D3 | semidirect |
| 27. #6706 | D3 | semidirect |
| 48. #3743 | D5 | semidirect |
| 57. D60 | C2×D3 | semidirect |
| 58. Dic30 | C2×D3 | semidirect |
| 73. C3×C5×C8 | C2×D3 | semidirect |
| 74. C3×C5×C8 | C2×D3 | semidirect |
| 101. C32×C8 | C2×D5 | semidirect |
| 102. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 148. C5×C8 | D32 | semidirect |
| 190. C3×C8 | D3×D5 | semidirect |
| 191. C3×C8 | D3×D5 | semidirect |
| 216. C3×C5 | #911 | semidirect |
| 217. C3×C5 | #914 | semidirect |
| 242. C32 | #4054 | semidirect |
| 253. C8 | (C3⋊D3)⋊D5 | semidirect |
| 266. C5 | #63798 | semidirect |
| 276. C3 | #91253 | semidirect |
| 277. C3 | #91254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624227 | 2 |
| #10624220 | 2 |
| C5×#3743 | 2 |
| C3×D120 | 2 |
| C3×#6706 | 2 |
| #10623825 | 2 |
| #10623822 | 2 |
| #91254 | 3 |
| #91253 | 3 |
| #63798 | 5 |