Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22608687 | C2 | semidirect |
| 4. #22608619 | C2 | semidirect |
| 5. #22608387 | C2 | semidirect |
| 6. #22607806 | C2 | semidirect |
| 189. C73 | #10460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619728 | 2 |
| #22609923 | 2 |
| #22608687 | 2 |
| #22608619 | 2 |
| #22608387 | 2 |
| #22607806 | 2 |
| C2×D4⋊C8×C73 | 2 |
| #10460 | 73 |