Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
516 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 189 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. #29504654 | C2 | semidirect |
| 4. #29504623 | C2 | semidirect |
| 6. C42×Dic239 | C2 | semidirect |
| 7. #383×C239 | C2 | semidirect |
| 9. #21439954 | C4 | semidirect |
| 28. Dic239⋊C4 | C2×C4 | semidirect |
| 37. C42×C239 | C2×C4 | semidirect |
| 68. Dic239 | #126 | semidirect |
| 73. C239 | C4×#126 | semidirect |
| 78. #383 | D239 | semidirect |
| 111. C42 | C4×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439954 | 2 |
| #29504661 | 2 |
| #29504654 | 2 |
| #29504623 | 2 |
| #29504619 | 2 |
| C42×Dic239 | 2 |
| #383×C239 | 2 |
| C4×#126 | 239 |