Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
554 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22617913 | C2 | semidirect |
| 2. #22611166 | C2 | semidirect |
| 3. #22611018 | C2 | semidirect |
| 5. #22607755 | C2 | semidirect |
| 6. #22607751 | C2 | semidirect |
| 7. C73×#1272 | C2 | semidirect |
| 236. #1272 | D73 | semidirect |
| 239. C73 | #7746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617913 | 2 |
| #22611166 | 2 |
| #22611018 | 2 |
| #22611004 | 2 |
| #22607755 | 2 |
| #22607751 | 2 |
| C73×#1272 | 2 |
| #7746 | 73 |