Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
412 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #22607944 | C2 | semidirect |
| 5. #22607943 | C2 | semidirect |
| 6. #22607942 | C2 | semidirect |
| 7. C73×#1348 | C2 | semidirect |
| 8. C2×Q16×D73 | C4 | semidirect |
| 12. #17988829 | C4 | semidirect |
| 16. #17988825 | C4 | semidirect |
| 17. #107×D73 | C4 | semidirect |
| 192. #1348 | D73 | semidirect |
| 193. C73 | #11889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D73 | 2 |
| #22611540 | 2 |
| #22609955 | 2 |
| #22607944 | 2 |
| #22607943 | 2 |
| #22607942 | 2 |
| C73×#1348 | 2 |
| #11889 | 73 |