Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
560 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22616052 | C2 | semidirect |
| 3. #22608656 | C2 | semidirect |
| 4. #22608533 | C2 | semidirect |
| 6. #22607823 | C2 | semidirect |
| 184. C73 | #10091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620391 | 2 |
| #22616052 | 2 |
| #22608656 | 2 |
| #22608533 | 2 |
| #22608439 | 2 |
| #22607823 | 2 |
| C73×#3234 | 2 |
| #10091 | 73 |