Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 2. C2×#17989508 | C2 | semidirect |
| 4. #22624970 | C2 | semidirect |
| 56. C22⋊Dic73 | C16 | semidirect |
| 89. C2×Dic73 | C2×C16 | semidirect |
| 99. C22×C73 | C4⋊C16 | semidirect |
| 123. C73 | #12912 | semidirect |
| 217. C22 | #17989508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924031 | 2 |
| C2×#17989508 | 2 |
| C2×C22⋊#11924031 | 2 |
| #22624970 | 2 |
| #22609705 | 2 |
| #12912 | 73 |