Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 154. C71 | #10528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599731 | 2 |
| #22588514 | 2 |
| #22587068 | 2 |
| #22586956 | 2 |
| #22586955 | 2 |
| #22586250 | 2 |
| C71×#1559 | 2 |
| #10528 | 71 |