Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
628 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 3. #99×#64408 | C2 | semidirect |
| 4. #22625024 | C2 | semidirect |
| 6. C2×D4×#64408 | C4 | semidirect |
| 9. #17989539 | C4 | semidirect |
| 13. #17989531 | C4 | semidirect |
| 15. #17989523 | C4 | semidirect |
| 16. #17989492 | C4 | semidirect |
| 17. #17989491 | C4 | semidirect |
| 21. #17988380 | C4 | semidirect |
| 22. #17988379 | C4 | semidirect |
| 23. #353×C73 | C4 | semidirect |
| 38. #14556650 | C2×C4 | semidirect |
| 53. #14556506 | C2×C4 | semidirect |
| 56. #99×C73 | C2×C4 | semidirect |
| 82. C2×D292 | C42 | semidirect |
| 100. C4×Dic73 | C42 | semidirect |
| 102. C2×D4×C73 | C42 | semidirect |
| 105. C42×C73 | C42 | semidirect |
| 204. C73 | #12628 | semidirect |
| 221. #353 | #64408 | semidirect |
| 251. #99 | C2×#64408 | semidirect |
| 272. C2×D4 | C4×#64408 | semidirect |
| 304. C42 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626423 | 2 |
| D73⋊#353 | 2 |
| #99×#64408 | 2 |
| #22625024 | 2 |
| #353×D73 | 2 |
| #12628 | 73 |