Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
190 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #22625097 | C2 | semidirect |
| 4. #22625096 | C2 | semidirect |
| 14. #17988421 | C4 | semidirect |
| 16. C32×D73 | C4 | semidirect |
| 17. M64×C73 | C4 | semidirect |
| 31. #14556497 | C2×C4 | semidirect |
| 33. C32×C73 | C2×C4 | semidirect |
| 80. D73 | #1426 | semidirect |
| 86. C73 | C2×#1426 | semidirect |
| 92. M64 | #64408 | semidirect |
| 114. C32 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#368 | 2 |
| C2×#17989514 | 2 |
| #22625097 | 2 |
| #22625096 | 2 |
| M64×D73 | 2 |
| C2×#1426 | 73 |