Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #29504781 | C2 | semidirect |
| 5. #29504541 | C2 | semidirect |
| 6. #29504532 | C2 | semidirect |
| 7. #391×C239 | C2 | semidirect |
| 10. #21439991 | C4 | semidirect |
| 42. #16838532 | C2×C4 | semidirect |
| 57. C2×Q8×C239 | C2×C4 | semidirect |
| 124. C239 | #1882 | semidirect |
| 130. #391 | D239 | semidirect |
| 163. C2×Q8 | C4×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439991 | 2 |
| #29505253 | 2 |
| C2×#21439888 | 2 |
| #29504781 | 2 |
| #29504541 | 2 |
| #29504532 | 2 |
| #391×C239 | 2 |
| #1882 | 239 |