Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
376 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. #22626168 | C2 | semidirect |
| 2. #22625813 | C2 | semidirect |
| 3. #22624903 | C2 | semidirect |
| 4. #22624901 | C2 | semidirect |
| 14. #17988842 | C4 | semidirect |
| 16. #17988837 | C4 | semidirect |
| 20. C2×#14556523 | C4 | semidirect |
| 22. C2×#135×C73 | C4 | semidirect |
| 177. C73 | #11867 | semidirect |
| 178. C2×#135 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626168 | 2 |
| #22625813 | 2 |
| #22624903 | 2 |
| #22624901 | 2 |
| #22619589 | 2 |
| #11867 | 73 |