Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. #22626622 | C2 | semidirect |
| 2. #22625838 | C2 | semidirect |
| 5. #22624803 | C2 | semidirect |
| 6. #22624773 | C2 | semidirect |
| 28. C2×#14556524 | C4 | semidirect |
| 29. C2×#14556523 | C4 | semidirect |
| 30. C2×#14556512 | C4 | semidirect |
| 32. C2×#102×C73 | C4 | semidirect |
| 231. C73 | #9242 | semidirect |
| 245. C2×#102 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626622 | 2 |
| #22625838 | 2 |
| #22625327 | 2 |
| #22625206 | 2 |
| #22624803 | 2 |
| #22624773 | 2 |
| C2×#17988910 | 2 |
| #9242 | 73 |