Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 27. C239⋊C16 | Q8 | semidirect |
| 31. C16×C239 | Q8 | semidirect |
| 55. C239 | #2255 | semidirect |
| 87. C16 | Dic478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29505176 | 2 |
| #29505173 | 2 |
| #29504600 | 2 |
| #29504599 | 2 |
| #29504597 | 2 |
| #29504547 | 2 |
| #366×C239 | 2 |
| #2255 | 239 |