Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #22625004 | C2 | semidirect |
| 4. #22624998 | C2 | semidirect |
| 17. #17988625 | C4 | semidirect |
| 18. #17988622 | C4 | semidirect |
| 20. #106×D73 | C4 | semidirect |
| 22. C2×#106×C73 | C4 | semidirect |
| 160. C73 | #12873 | semidirect |
| 173. C2×#106 | #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 |
| #22625004 | 2 |
| #22624998 | 2 |
| #22618522 | 2 |
| #12873 | 73 |