Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 128 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. C2×#67180 | C2 | semidirect |
| 3. C2×C5×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #10623762 | C2 | direct (N × H) |
| 10. #67180 | C22 | semidirect |
| 13. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 29. C2×C3⋊(C3⋊C8) | D5 | semidirect |
| 39. C2×C32×C5 | SD16 | semidirect |
| 53. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 64. C32×C5 | C2×SD16 | semidirect |
| 80. C2×C3×C5 | #214 | semidirect |
| 98. C2×C32 | #677 | semidirect |
| 104. C3×C5 | C2×#214 | semidirect |
| 111. C2×C5 | #3754 | semidirect |
| 114. C32 | C2×#677 | semidirect |
| 124. C2×C3 | #6657 | semidirect |
| 126. C5 | C2×#3754 | semidirect |
| 133. C3 | C2×#6657 | semidirect |
| 135. C2 | #10623762 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67180 | 2 |
| C2×C32×D20 | 2 |
| C2×C5×C3⋊(C3⋊C8) | 2 |
| #10623762 | 2 |
| C2×#6657 | 3 |
| C2×#3754 | 5 |