Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
364 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22617688 | C2 | semidirect |
| 5. #22607962 | C2 | semidirect |
| 6. #22607938 | C2 | semidirect |
| 7. C73×#1324 | C2 | semidirect |
| 179. #1324 | D73 | semidirect |
| 180. C73 | #12143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617688 | 2 |
| #22611160 | 2 |
| #22608936 | 2 |
| #22608902 | 2 |
| #22607962 | 2 |
| #22607938 | 2 |
| C73×#1324 | 2 |
| #12143 | 73 |