Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
148 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D5×D11 |
| commutator, socle, cosocle | C22×C5×C11 | C23 |
| Fitting, prime radical | C23×C5×C11 | C22 |
| hypercenter | C23 | D5×D11 |
| hypocenter | C5×C11 | C22⋊Q8 |
| LCS | G ▷ C22×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#89170 | C2 | semidirect |
| 5. #11724889 | C2 | semidirect |
| 6. #11724888 | C2 | semidirect |
| 7. Dic11⋊Dic5 | C2 | semidirect |
| 20. C22×C5×C11 | Q8 | semidirect |
| 56. C5×C11 | C22⋊Q8 | semidirect |
| 59. C22×C11 | Dic10 | semidirect |
| 83. C22×C5 | Dic22 | semidirect |
| 98. C11 | #4070 | semidirect |
| 112. C5 | #66931 | semidirect |
| 115. C22 | #89170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic11 | 2 |
| C2×#89170 | 2 |
| C22⋊Dic55 | 2 |
| C11×C22⋊Dic5 | 2 |
| #11724889 | 2 |
| #11724888 | 2 |
| Dic11⋊Dic5 | 2 |
| #66931 | 5 |
| #4070 | 11 |