Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
338 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32×D5 |
| commutator | C2×C32×C5 | C22×C4 |
| Fitting, socle, cosocle | C22×C32×C5 | C23 |
| prime radical | C22×C5×C3⋊D3 | C22 |
| hypocenter | C32×C5 | #117 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10623814 | C2 | semidirect |
| 3. Dic3×Dic15 | C2 | semidirect |
| 6. C3×#6669 | C2 | semidirect |
| 7. C3×Dic3×Dic5 | C2 | semidirect |
| 17. #67155 | C4 | semidirect |
| 27. #6669 | D3 | semidirect |
| 33. Dic3×Dic5 | D3 | semidirect |
| 133. C32×C5 | #117 | semidirect |
| 206. C3×C5 | #872 | semidirect |
| 207. C3×C5 | #892 | semidirect |
| 238. C32 | #4023 | semidirect |
| 259. C5 | #63836 | semidirect |
| 271. C3 | #91398 | semidirect |
| 272. C3 | #91400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67155 | 2 |
| #10623814 | 2 |
| Dic3×Dic15 | 2 |
| C5×#3722 | 2 |
| #10623771 | 2 |
| C3×#6669 | 2 |
| C3×Dic3×Dic5 | 2 |
| #91400 | 3 |
| #91398 | 3 |
| #63836 | 5 |