Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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. #29504597 | C2 | semidirect |
| 4. #29504576 | C2 | semidirect |
| 6. #29504548 | C2 | semidirect |
| 7. C4×Q16×C239 | C2 | semidirect |
| 10. #21439903 | C4 | semidirect |
| 27. C239⋊C16 | C2×C4 | semidirect |
| 30. Q16×C239 | C2×C4 | semidirect |
| 67. C239 | #2175 | semidirect |
| 70. C4×Q16 | D239 | semidirect |
| 92. Q16 | C4×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439903 | 2 |
| C4×D1912 | 2 |
| #29504597 | 2 |
| #29504576 | 2 |
| #29504572 | 2 |
| #29504548 | 2 |
| C4×Q16×C239 | 2 |
| #2175 | 239 |