Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 1. #22626264 | C2 | semidirect |
| 3. #22625871 | C2 | semidirect |
| 4. #22625005 | C2 | semidirect |
| 171. Dic73 | #361 | semidirect |
| 187. C73 | #12818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626264 | 2 |
| C2×#17989505 | 2 |
| #22625871 | 2 |
| #22625005 | 2 |
| C4×D8×D73 | 2 |
| #12818 | 73 |