Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 508 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. #22610857 | C2 | semidirect |
| 3. #22610850 | C2 | semidirect |
| 4. #22610771 | C2 | semidirect |
| 5. #22608606 | C2 | semidirect |
| 6. #22607833 | C2 | semidirect |
| 7. C73×#1565 | C2 | semidirect |
| 115. M16×C73 | D8 | semidirect |
| 212. #1565 | D73 | semidirect |
| 215. C73 | #10500 | semidirect |
| 314. M16 | D584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620851 | 2 |
| #22610857 | 2 |
| #22610850 | 2 |
| #22610771 | 2 |
| #22608606 | 2 |
| #22607833 | 2 |
| C73×#1565 | 2 |
| #10500 | 73 |