Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22627055 | C2 | semidirect |
| 3. #22626935 | C2 | semidirect |
| 43. C22×#10596831 | C8 | semidirect |
| 48. C2×C8×D73 | C8 | semidirect |
| 49. C2×C8×D73 | C8 | semidirect |
| 52. C22×C8×C73 | C8 | semidirect |
| 179. C73 | #8601 | semidirect |
| 210. C22×C8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627055 | 2 |
| #22627043 | 2 |
| #22626935 | 2 |
| C2×#17989550 | 2 |
| #8601 | 73 |