Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1482 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 227 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. #22609999 | C2 | semidirect |
| 2. C2×#17988311 | C2 | semidirect |
| 21. C22×D4×C73 | C8 | semidirect |
| 158. C73 | #8302 | semidirect |
| 174. C22×D4 | #10596831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609999 | 2 |
| C2×#17988311 | 2 |
| C22×C4×D4×C73 | 2 |
| #8302 | 73 |