Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 2. #22626074 | C2 | semidirect |
| 3. #22625446 | C2 | semidirect |
| 5. #22624839 | C2 | semidirect |
| 6. #22624815 | C2 | semidirect |
| 136. Q8×C73 | #101 | semidirect |
| 208. C73 | #9358 | semidirect |
| 340. Q8 | #14556652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626863 | 2 |
| #22626074 | 2 |
| #22625446 | 2 |
| #22625266 | 2 |
| #22624839 | 2 |
| #22624815 | 2 |
| #22619742 | 2 |
| #9358 | 73 |