Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
784 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22609874 | C2 | semidirect |
| 3. C4×#14556506 | C2 | semidirect |
| 4. #22607816 | C2 | semidirect |
| 5. C73×#2973 | C2 | semidirect |
| 10. #17988507 | C4 | semidirect |
| 11. #17988504 | C4 | semidirect |
| 13. #17988499 | C4 | semidirect |
| 14. #17988496 | C4 | semidirect |
| 53. C2×M16×C73 | D4 | semidirect |
| 131. C23×C73 | #104 | semidirect |
| 220. #2973 | D73 | semidirect |
| 225. C73 | #9009 | semidirect |
| 256. C2×M16 | C22⋊D73 | semidirect |
| 358. C23 | #14556517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613146 | 2 |
| #22609874 | 2 |
| C4×#14556506 | 2 |
| #22607816 | 2 |
| C73×#2973 | 2 |
| #9009 | 73 |