Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
542 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 78 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. #22626442 | C2 | semidirect |
| 3. #22625839 | C2 | semidirect |
| 5. #22624831 | C2 | semidirect |
| 6. #22624811 | C2 | semidirect |
| 28. #17988627 | C4 | semidirect |
| 29. #17988593 | C4 | semidirect |
| 30. #17988591 | C4 | semidirect |
| 32. #428×C73 | C4 | semidirect |
| 245. C73 | #9366 | semidirect |
| 253. #428 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626442 | 2 |
| #22626071 | 2 |
| #22625839 | 2 |
| #22625328 | 2 |
| #22624831 | 2 |
| #22624811 | 2 |
| #22619873 | 2 |
| #9366 | 73 |