Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
432 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 96 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. C4×#14556659 | C2 | semidirect |
| 3. #22625490 | C2 | semidirect |
| 4. #22624828 | C2 | semidirect |
| 15. #17988718 | C4 | semidirect |
| 16. #17988666 | C4 | semidirect |
| 17. #17988664 | C4 | semidirect |
| 24. #446×C73 | C4 | semidirect |
| 138. #10596831 | #104 | semidirect |
| 169. C73 | #8669 | semidirect |
| 172. #446 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625804 | 2 |
| C4×#14556659 | 2 |
| #22625490 | 2 |
| #22624828 | 2 |
| #22618896 | 2 |
| #8669 | 73 |