Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22626290 | C2 | semidirect |
| 2. #22625853 | C2 | semidirect |
| 3. #22624919 | C2 | semidirect |
| 13. #17988989 | C4 | semidirect |
| 18. Q16×Dic73 | C4 | semidirect |
| 20. D8×Dic73 | C4 | semidirect |
| 22. #495×C73 | C4 | semidirect |
| 147. C73 | #11855 | semidirect |
| 150. #495 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626290 | 2 |
| #22625853 | 2 |
| #22624919 | 2 |
| #22624917 | 2 |
| #22620498 | 2 |
| #11855 | 73 |