Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22627135 | C2 | semidirect |
| 2. #22627130 | C2 | semidirect |
| 3. #22626976 | C2 | semidirect |
| 4. #22626975 | C2 | semidirect |
| 7. #17989690 | C22 | semidirect |
| 10. #17989681 | C22 | semidirect |
| 162. C73 | #11634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627135 | 2 |
| #22627130 | 2 |
| #22626976 | 2 |
| #22626975 | 2 |
| D73⋊#436 | 2 |
| #11634 | 73 |