Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 172 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 |
|---|---|---|
| 65. C4×C73 | #364 | semidirect |
| 77. C73 | #12900 | semidirect |
| 140. C4 | #17989509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989509 | 2 |
| #22626263 | 2 |
| C4×C8×Dic73 | 2 |
| #12900 | 73 |