Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22612251 | C2 | semidirect |
| 3. #22612192 | C2 | semidirect |
| 4. #22611813 | C2 | semidirect |
| 5. #22608125 | C2 | semidirect |
| 6. #22608122 | C2 | semidirect |
| 7. C73×#1422 | C2 | semidirect |
| 101. #1422 | D73 | semidirect |
| 104. C73 | #13691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612251 | 2 |
| #22612246 | 2 |
| #22612192 | 2 |
| #22611813 | 2 |
| #22608125 | 2 |
| #22608122 | 2 |
| C73×#1422 | 2 |
| #13691 | 73 |