Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
648 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#17988982 | C2 | semidirect |
| 2. C2×#17988946 | C2 | semidirect |
| 3. #22610903 | C2 | semidirect |
| 4. C2×#17988327 | C2 | semidirect |
| 5. C2×#17988327 | C2 | semidirect |
| 6. #22607812 | C2 | semidirect |
| 42. #14556591 | D4 | semidirect |
| 51. #14556502 | D4 | semidirect |
| 52. #14556502 | D4 | semidirect |
| 218. C73 | #10081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988982 | 2 |
| C2×#17988946 | 2 |
| #22610903 | 2 |
| C2×#17988327 | 2 |
| #22607812 | 2 |
| C73×#2819 | 2 |
| #10081 | 73 |