Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. C4×#16838532 | C2 | semidirect |
| 4. #29504540 | C2 | semidirect |
| 5. C4×M16×C239 | C2 | semidirect |
| 15. #21439876 | C4 | direct (N × H) |
| 32. #16838532 | C2×C4 | semidirect |
| 42. M16×C239 | C2×C4 | semidirect |
| 85. C4×C239 | #100 | semidirect |
| 95. C239 | C4×#100 | semidirect |
| 100. C4×M16 | D239 | semidirect |
| 133. M16 | C4×D239 | semidirect |
| 182. C4 | #21439876 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D956 | 2 |
| C2×#21439876 | 2 |
| C4×#16838532 | 2 |
| #29504540 | 2 |
| C4×M16×C239 | 2 |
| C4×#100 | 239 |