Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
180 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 51. C8×C239 | Q16 | semidirect |
| 63. C239 | #1707 | semidirect |
| 115. C8 | #16838538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29505175 | 2 |
| #29505170 | 2 |
| #29505151 | 2 |
| #29505124 | 2 |
| #29505122 | 2 |
| C8×C239⋊C8 | 2 |
| #498×C239 | 2 |
| #1707 | 239 |