Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 23. #17988404 | C4 | semidirect |
| 24. #17988403 | C4 | semidirect |
| 25. #17988402 | C4 | semidirect |
| 26. #362×C73 | C4 | semidirect |
| 165. C73 | #13135 | semidirect |
| 181. #362 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626283 | 2 |
| #22626241 | 2 |
| #22626077 | 2 |
| #22625736 | 2 |
| #22625007 | 2 |
| #22624974 | 2 |
| #362×D73 | 2 |
| #13135 | 73 |