Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
270 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 16. #17988309 | C4 | semidirect |
| 17. #17988308 | C4 | semidirect |
| 132. C73 | #8794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610102 | 2 |
| #22610061 | 2 |
| #22608224 | 2 |
| #22607791 | 2 |
| #22607790 | 2 |
| #22607789 | 2 |
| C73×#1286 | 2 |
| #8794 | 73 |