Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
274 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 88. #10596831 | Q32 | semidirect |
| 109. C73 | #12528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612183 | 2 |
| #22612159 | 2 |
| #22612158 | 2 |
| #22609547 | 2 |
| #22609525 | 2 |
| #22607850 | 2 |
| C73×#2247 | 2 |
| #12528 | 73 |