Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
958 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 2. C2×#17988957 | C2 | semidirect |
| 3. C2×#17988947 | C2 | semidirect |
| 4. #22609255 | C2 | direct (N × H) |
| 5. C2×#17988326 | C2 | semidirect |
| 6. C2×#330×C73 | C2 | semidirect |
| 16. #17988957 | C22 | semidirect |
| 18. #17988947 | C22 | semidirect |
| 23. #17988326 | C22 | semidirect |
| 26. #330×C73 | C22 | semidirect |
| 145. C2×C73 | #1662 | semidirect |
| 153. C2×#330 | D73 | semidirect |
| 155. C73 | C2×#1662 | semidirect |
| 174. #330 | C2×D73 | semidirect |
| 294. C2 | #22609255 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989335 | 2 |
| C2×#17988957 | 2 |
| C2×#17988947 | 2 |
| #22609255 | 2 |
| C2×#17988326 | 2 |
| C2×#330×C73 | 2 |
| C2×#1662 | 73 |