Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22611540 | C2 | semidirect |
| 3. #340×D73 | C2 | semidirect |
| 4. #22607943 | C2 | semidirect |
| 5. #22607941 | C2 | semidirect |
| 6. #22607939 | C2 | semidirect |
| 7. C73×#1348 | C2 | semidirect |
| 8. C2×#14556614 | C4 | semidirect |
| 13. #17988825 | C4 | semidirect |
| 14. #17988824 | C4 | semidirect |
| 18. #17988624 | C4 | semidirect |
| 32. C2×D584 | C2×C4 | semidirect |
| 53. #14556525 | C2×C4 | semidirect |
| 58. C2×Q16×C73 | C2×C4 | semidirect |
| 63. #107×C73 | C2×C4 | semidirect |
| 200. #1348 | D73 | semidirect |
| 203. C73 | #11704 | semidirect |
| 227. C2×Q16 | C4×D73 | semidirect |
| 255. #107 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619514 | 2 |
| #22611540 | 2 |
| #340×D73 | 2 |
| #22607943 | 2 |
| #22607941 | 2 |
| #22607939 | 2 |
| C73×#1348 | 2 |
| #11704 | 73 |