Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 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. #22612654 | C2 | semidirect |
| 3. #22610762 | C2 | semidirect |
| 4. #22608600 | C2 | semidirect |
| 5. #22608490 | C2 | semidirect |
| 6. #22607759 | C2 | semidirect |
| 7. C73×#1286 | C2 | semidirect |
| 11. #17988964 | C4 | semidirect |
| 12. #17988934 | C4 | semidirect |
| 33. #14556591 | C2×C4 | semidirect |
| 37. #14556588 | C2×C4 | semidirect |
| 66. C4×C8×C73 | C2×C4 | semidirect |
| 109. C4×Dic73 | D8 | semidirect |
| 217. #1286 | D73 | semidirect |
| 219. C73 | #9299 | semidirect |
| 276. C4×C8 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620851 | 2 |
| #22612654 | 2 |
| #22610762 | 2 |
| #22608600 | 2 |
| #22608490 | 2 |
| #22607759 | 2 |
| C73×#1286 | 2 |
| #9299 | 73 |