Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
262 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 262 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 |
|---|---|---|
| 105. C71 | #12510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590569 | 2 |
| #22590568 | 2 |
| #22590567 | 2 |
| #22587957 | 2 |
| #22587956 | 2 |
| C16×C71⋊C8 | 2 |
| C71×#2241 | 2 |
| #12510 | 71 |