Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1146 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 203 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. #22608322 | C2 | semidirect |
| 2. #22608245 | C2 | semidirect |
| 4. #17988640 | C22 | semidirect |
| 24. C22×D4×C73 | C8 | semidirect |
| 154. C73 | #8322 | semidirect |
| 172. C22×D4 | #10596831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22608322 | 2 |
| #22608245 | 2 |
| C2×#518×C73 | 2 |
| #8322 | 73 |