Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
678 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 178 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×Dic30 | C2 | semidirect |
| 3. C2×C3×C5×Dic6 | C2 | semidirect |
| 4. C2×#67153 | C2 | semidirect |
| 6. #10624198 | C2 | direct (N × H) |
| 14. C3×Dic30 | C22 | semidirect |
| 16. C3×C5×Dic6 | C22 | semidirect |
| 17. #67153 | C22 | semidirect |
| 27. C2×Dic30 | D3 | semidirect |
| 28. C2×C5×Dic6 | D3 | semidirect |
| 34. C2×C3⋊D15 | Q8 | semidirect |
| 43. C2×C3×Dic6 | D5 | semidirect |
| 64. Dic30 | C2×D3 | semidirect |
| 66. C5×Dic6 | C2×D3 | semidirect |
| 73. C2×C32×C5 | C2×Q8 | semidirect |
| 75. C3⋊D15 | C2×Q8 | semidirect |
| 89. C3×Dic6 | C2×D5 | semidirect |
| 123. C2×Dic6 | D15 | semidirect |
| 124. C32×C5 | C22×Q8 | semidirect |
| 145. C2×C3×C5 | D3×Q8 | semidirect |
| 146. C2×C3×C5 | D3×Q8 | semidirect |
| 175. Dic6 | C2×D15 | semidirect |
| 183. C2×C32 | Q8×D5 | semidirect |
| 193. C3×C5 | C2×D3×Q8 | semidirect |
| 194. C3×C5 | C2×D3×Q8 | semidirect |
| 214. C2×C5 | #3797 | semidirect |
| 217. C32 | C2×Q8×D5 | semidirect |
| 230. C2×C3 | D15⋊Q8 | semidirect |
| 231. C2×C3 | Q8×D15 | semidirect |
| 237. C5 | C2×#3797 | semidirect |
| 246. C3 | C2×D15⋊Q8 | semidirect |
| 247. C3 | C2×Q8×D15 | semidirect |
| 249. C2 | #10624198 | 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×Dic30 | 2 |
| C2×C3×C5×Dic6 | 2 |
| C2×#67153 | 2 |
| C2×#67149 | 2 |
| #10624198 | 2 |
| C2×Q8×D15 | 3 |
| C2×D15⋊Q8 | 3 |
| C2×#3797 | 5 |