Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #29504796 | C2 | semidirect |
| 3. C2×#21439888 | C2 | semidirect |
| 4. C43×C239 | C2 | semidirect |
| 7. #21439960 | C4 | semidirect |
| 8. #21439957 | C4 | semidirect |
| 9. #21439948 | C4 | semidirect |
| 36. C42×C239 | D4 | semidirect |
| 63. C4×C239 | #104 | semidirect |
| 72. C239 | #1962 | semidirect |
| 77. C43 | D239 | semidirect |
| 109. C42 | D956 | semidirect |
| 137. C4 | #21439888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29505322 | 2 |
| #29504796 | 2 |
| C2×#21439888 | 2 |
| C43×C239 | 2 |
| #1962 | 239 |