Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22620930 | C2 | semidirect |
| 3. #22609246 | C2 | semidirect |
| 4. #22608558 | C2 | semidirect |
| 5. #22608528 | C2 | semidirect |
| 6. C73×#3166 | C2 | semidirect |
| 14. #17988979 | C22 | semidirect |
| 15. #17988949 | C22 | semidirect |
| 20. #17988329 | C22 | semidirect |
| 21. #17988326 | C22 | semidirect |
| 24. #501×C73 | C22 | semidirect |
| 154. #3166 | D73 | semidirect |
| 158. C73 | #19006 | semidirect |
| 168. #501 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989335 | 2 |
| #22620930 | 2 |
| #22609246 | 2 |
| #22608558 | 2 |
| #22608528 | 2 |
| C73×#3166 | 2 |
| #19006 | 73 |