Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
186 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22611813 | C2 | semidirect |
| 3. #22608134 | C2 | semidirect |
| 4. #22608115 | C2 | semidirect |
| 5. #22608114 | C2 | semidirect |
| 6. C4×#14556497 | C2 | semidirect |
| 7. C73×#2178 | C2 | semidirect |
| 10. #17988427 | C4 | semidirect |
| 11. #17988425 | C4 | semidirect |
| 12. #17988424 | C4 | semidirect |
| 13. #17988422 | C4 | semidirect |
| 94. #2178 | D73 | semidirect |
| 99. C73 | #13655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612238 | 2 |
| #22611813 | 2 |
| #22608134 | 2 |
| #22608115 | 2 |
| #22608114 | 2 |
| C4×#14556497 | 2 |
| C73×#2178 | 2 |
| #13655 | 73 |