Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
392 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22625497 | C2 | semidirect |
| 4. #22625496 | C2 | semidirect |
| 5. #22624820 | C2 | semidirect |
| 6. #22624820 | C2 | semidirect |
| 27. #17988327 | C4 | semidirect |
| 28. #17988326 | C4 | semidirect |
| 29. #17988326 | C4 | semidirect |
| 30. #329×C73 | C4 | semidirect |
| 194. C73 | #8918 | semidirect |
| 217. #329 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626817 | 2 |
| #22626068 | 2 |
| #22625497 | 2 |
| #22625496 | 2 |
| #22624820 | 2 |
| #22608521 | 2 |
| #8918 | 73 |