Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
182 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 3. #22611802 | C2 | semidirect |
| 4. #22608138 | C2 | semidirect |
| 6. #22608066 | C2 | semidirect |
| 7. C73×#1420 | C2 | semidirect |
| 11. #17988427 | C4 | semidirect |
| 12. #17988424 | C4 | semidirect |
| 88. #1420 | D73 | semidirect |
| 91. C73 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612249 | 2 |
| #22611816 | 2 |
| #22611802 | 2 |
| #22608138 | 2 |
| #22608119 | 2 |
| #22608066 | 2 |
| C73×#1420 | 2 |
| #13657 | 73 |