Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 3. C3×#6718 | C2 | semidirect |
| 4. C3×C5×#216 | C2 | semidirect |
| 5. #10623809 | C2 | semidirect |
| 6. #10623808 | C2 | semidirect |
| 29. #6718 | D3 | semidirect |
| 32. C5×#216 | D3 | semidirect |
| 48. C3×#216 | D5 | semidirect |
| 82. C3⋊D15 | Q16 | semidirect |
| 130. #216 | D15 | semidirect |
| 135. C32×C5 | C2×Q16 | semidirect |
| 205. C3×C5 | D3×Q16 | semidirect |
| 206. C3×C5 | D3×Q16 | semidirect |
| 228. C32 | D5×Q16 | semidirect |
| 246. C5 | #63944 | semidirect |
| 255. C3 | #91511 | semidirect |
| 256. C3 | Q16×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊D15 | 2 |
| #10624198 | 2 |
| C3×#6718 | 2 |
| C3×C5×#216 | 2 |
| #10623809 | 2 |
| #10623808 | 2 |
| #10623794 | 2 |
| Q16×D15 | 3 |
| #91511 | 3 |
| #63944 | 5 |