Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
754 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22610920 | C2 | semidirect |
| 3. #22610775 | C2 | semidirect |
| 4. #22608666 | C2 | semidirect |
| 5. #22608371 | C2 | semidirect |
| 6. #22608371 | C2 | semidirect |
| 7. C73×#1525 | C2 | semidirect |
| 239. #1525 | D73 | semidirect |
| 242. C73 | #8470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623838 | 2 |
| #22610920 | 2 |
| #22610775 | 2 |
| #22608666 | 2 |
| #22608371 | 2 |
| C73×#1525 | 2 |
| #8470 | 73 |