Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
364 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 70 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. #22624904 | C2 | semidirect |
| 4. #22624903 | C2 | semidirect |
| 12. C2×Q16×D73 | C4 | semidirect |
| 16. #17988845 | C4 | semidirect |
| 20. #17988622 | C4 | semidirect |
| 22. #470×C73 | C4 | semidirect |
| 171. C73 | #11869 | semidirect |
| 179. #470 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626169 | 2 |
| #22625814 | 2 |
| #22624904 | 2 |
| #22624903 | 2 |
| #22619584 | 2 |
| #11869 | 73 |