Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. C3×#6819 | C2 | semidirect |
| 2. #10624224 | C2 | semidirect |
| 3. C5×#3753 | C2 | semidirect |
| 4. C3×#6716 | C2 | semidirect |
| 5. #10623827 | C2 | semidirect |
| 6. #10623824 | C2 | semidirect |
| 7. #10623817 | C2 | semidirect |
| 22. #6819 | D3 | semidirect |
| 26. #6716 | D3 | semidirect |
| 47. #3753 | D5 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 208. C3×C5 | #916 | semidirect |
| 209. C3×C5 | #950 | semidirect |
| 231. C32 | #4058 | semidirect |
| 254. C5 | #63935 | semidirect |
| 263. C3 | #91490 | semidirect |
| 264. C3 | #91499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6819 | 2 |
| #10624224 | 2 |
| C5×#3753 | 2 |
| C3×#6716 | 2 |
| #10623827 | 2 |
| #10623824 | 2 |
| #10623817 | 2 |
| #91499 | 3 |
| #91490 | 3 |
| #63935 | 5 |