Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
540 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22620332 | C2 | semidirect |
| 3. #22615802 | C2 | semidirect |
| 4. #22608557 | C2 | semidirect |
| 5. #22608477 | C2 | semidirect |
| 6. #22608375 | C2 | semidirect |
| 7. C73×#1288 | C2 | semidirect |
| 209. #1288 | D73 | semidirect |
| 210. C73 | #10019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620332 | 2 |
| #22620023 | 2 |
| #22615802 | 2 |
| #22608557 | 2 |
| #22608477 | 2 |
| #22608375 | 2 |
| C73×#1288 | 2 |
| #10019 | 73 |