Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22608136 | C2 | semidirect |
| 4. #22608124 | C2 | semidirect |
| 6. #22608067 | C2 | semidirect |
| 7. C73×#2176 | C2 | semidirect |
| 10. #17988427 | C4 | semidirect |
| 11. #17988424 | C4 | semidirect |
| 86. #2176 | 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 |
| #22611818 | 2 |
| #22608136 | 2 |
| #22608124 | 2 |
| #22608117 | 2 |
| #22608067 | 2 |
| C73×#2176 | 2 |
| #13657 | 73 |