Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 98 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×C3×C5×C3⋊C8 | C2 | semidirect |
| 4. #10623797 | C2 | direct (N × H) |
| 12. C3×C3⋊#168 | C22 | semidirect |
| 13. C3×C5×C3⋊C8 | C22 | semidirect |
| 19. C2×C3⋊#168 | D3 | semidirect |
| 21. C2×C5×C3⋊C8 | D3 | semidirect |
| 33. C2×C3×C3⋊C8 | D5 | semidirect |
| 51. C3⋊#168 | C2×D3 | semidirect |
| 53. C5×C3⋊C8 | C2×D3 | semidirect |
| 56. C2×C32×C5 | M16 | semidirect |
| 69. C3×C3⋊C8 | C2×D5 | semidirect |
| 94. C2×C3⋊C8 | D15 | semidirect |
| 97. C32×C5 | C2×M16 | semidirect |
| 114. C2×C3×C5 | ΓL(1,𝔽25) | semidirect |
| 115. C2×C3×C5 | ΓL(1,𝔽25) | semidirect |
| 139. C3⋊C8 | C2×D15 | semidirect |
| 146. C2×C32 | #676 | semidirect |
| 154. C3×C5 | C2×ΓL(1,𝔽25) | semidirect |
| 155. C3×C5 | C2×ΓL(1,𝔽25) | semidirect |
| 174. C2×C5 | #3712 | semidirect |
| 177. C32 | C2×#676 | semidirect |
| 187. C2×C3 | #6651 | semidirect |
| 188. C2×C3 | #6705 | semidirect |
| 194. C5 | C2×#3712 | semidirect |
| 202. C3 | C2×#6651 | semidirect |
| 203. C3 | C2×#6705 | semidirect |
| 205. C2 | #10623797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊D15 | 2 |
| C2×C3×C3⋊#168 | 2 |
| C2×C3×C5×C3⋊C8 | 2 |
| #10623797 | 2 |
| C2×#6705 | 3 |
| C2×#6651 | 3 |
| C2×#3712 | 5 |