Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1168 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22609849 | C2 | semidirect |
| 3. #22608461 | C2 | semidirect |
| 4. C73×#1785 | C2 | semidirect |
| 5. C23×D292 | C4 | semidirect |
| 9. C2×#14556565 | C4 | semidirect |
| 13. C2×#14556550 | C4 | semidirect |
| 16. #17988450 | C22 | semidirect |
| 21. #407×C73 | C22 | semidirect |
| 210. #1785 | D73 | semidirect |
| 213. C73 | #8516 | semidirect |
| 228. #407 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989151 | 2 |
| #22609849 | 2 |
| #22608461 | 2 |
| C73×#1785 | 2 |
| #8516 | 73 |