Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #22610068 | C2 | semidirect |
| 3. #22608720 | C2 | semidirect |
| 6. #22607769 | C2 | semidirect |
| 7. C73×#1299 | C2 | semidirect |
| 172. #1299 | D73 | semidirect |
| 174. C73 | #8900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619057 | 2 |
| #22610068 | 2 |
| #22608720 | 2 |
| #22608371 | 2 |
| #22608311 | 2 |
| #22607769 | 2 |
| C73×#1299 | 2 |
| #8900 | 73 |