Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1786 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1786 conjugacy classes of subgroups — too many to draw. Only its 328 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 |
|---|---|---|
| 1. C24×#10596833 | C2 | semidirect |
| 2. C2×#17989614 | C2 | semidirect |
| 3. #22625906 | C2 | semidirect |
| 4. #22625875 | C2 | semidirect |
| 5. #22625753 | C2 | semidirect |
| 6. C22⋊C4×#10596833 | C2 | semidirect |
| 8. C22×#11924036 | C22 | semidirect |
| 13. C2×#14556658 | C22 | semidirect |
| 14. C2×#14556648 | C22 | semidirect |
| 17. C2×C4×#10596833 | C22 | semidirect |
| 18. #17989453 | C22 | semidirect |
| 31. C22×#10596833 | D4 | semidirect |
| 47. #14556560 | C8 | semidirect |
| 70. C2×C22⋊D73 | C2×C8 | semidirect |
| 85. C22⋊Dic73 | C2×C8 | semidirect |
| 91. C24×C73 | C2×C8 | semidirect |
| 108. C22×D73 | C22×C8 | semidirect |
| 121. C2×Dic73 | C22×C8 | semidirect |
| 129. #10596833 | #120 | semidirect |
| 135. C22×C73 | C8×D4 | semidirect |
| 161. C73 | C8×#120 | semidirect |
| 215. C24 | #11924036 | semidirect |
| 292. C22 | #17989614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#10596833 | 2 |
| C2×#17989614 | 2 |
| #22625906 | 2 |
| #22625875 | 2 |
| #22625753 | 2 |
| C22⋊C4×#10596833 | 2 |
| #22612430 | 2 |
| C8×#120 | 73 |