Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 2. C2×C3⋊(C3⋊#168) | C2 | semidirect |
| 3. C2×C5×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #10623754 | C2 | direct (N × H) |
| 11. C3⋊(C3⋊#168) | C22 | semidirect |
| 12. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 28. C2×C3⋊(C3⋊C8) | D5 | semidirect |
| 37. C2×C32×C5 | M16 | semidirect |
| 50. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 61. C32×C5 | C2×M16 | semidirect |
| 76. C2×C3×C5 | #208 | semidirect |
| 93. C2×C32 | #676 | semidirect |
| 99. C3×C5 | C2×#208 | semidirect |
| 106. C2×C5 | #3748 | semidirect |
| 109. C32 | C2×#676 | semidirect |
| 118. C2×C3 | #6649 | semidirect |
| 120. C5 | C2×#3748 | semidirect |
| 127. C3 | C2×#6649 | semidirect |
| 129. C2 | #10623754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×D5 | 2 |
| C2×C3⋊(C3⋊#168) | 2 |
| C2×C5×C3⋊(C3⋊C8) | 2 |
| #10623754 | 2 |
| C2×#6649 | 3 |
| C2×#3748 | 5 |