Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 63 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. C5×#3756 | C2 | semidirect |
| 4. C3×#6718 | C2 | semidirect |
| 5. #10623827 | C2 | semidirect |
| 6. #10623826 | C2 | semidirect |
| 26. #6718 | D3 | semidirect |
| 47. #3756 | D5 | semidirect |
| 80. C3×D15 | Q16 | semidirect |
| 131. C32×C5 | C2×Q16 | semidirect |
| 154. D15 | #216 | semidirect |
| 198. C3×C5 | D3×Q16 | semidirect |
| 199. C3×C5 | C2×#216 | semidirect |
| 219. C32 | D5×Q16 | semidirect |
| 236. C5 | D3×#216 | semidirect |
| 245. C3 | D5×#216 | semidirect |
| 246. C3 | #91511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D15 | 2 |
| #10624219 | 2 |
| C5×#3756 | 2 |
| C3×#6718 | 2 |
| #10623827 | 2 |
| #10623826 | 2 |
| #10623817 | 2 |
| #91511 | 3 |
| D5×#216 | 3 |
| D3×#216 | 5 |