Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
388 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4⋊Dic239 | C2 | semidirect |
| 4. #29504535 | C2 | semidirect |
| 5. C2×#97×C239 | C2 | semidirect |
| 9. C4×D956 | C4 | semidirect |
| 14. #21439882 | C4 | semidirect |
| 31. C4⋊Dic239 | C2×C4 | semidirect |
| 39. C2×C8×C239 | C2×C4 | semidirect |
| 49. D956 | C42 | semidirect |
| 90. C239 | #1762 | semidirect |
| 94. C2×#97 | D239 | semidirect |
| 124. C2×C8 | C4×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D956 | 2 |
| C2×#21439882 | 2 |
| C4×C4⋊Dic239 | 2 |
| #29504535 | 2 |
| C2×#97×C239 | 2 |
| #1762 | 239 |