Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
614 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 144 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. C22⋊C4×#10596833 | C2 | semidirect |
| 4. #22624774 | C2 | semidirect |
| 6. C22×#11924036 | C4 | semidirect |
| 10. C2×#14556658 | C4 | semidirect |
| 11. C2×#14556648 | C4 | semidirect |
| 15. C2×C4×#10596833 | C4 | semidirect |
| 17. #17989433 | C4 | semidirect |
| 18. #17989431 | C4 | semidirect |
| 53. #14556505 | C8 | semidirect |
| 92. C22⋊Dic73 | C2×C8 | semidirect |
| 104. C22⋊C4×C73 | C2×C8 | semidirect |
| 116. C22×D73 | C4×C8 | semidirect |
| 137. C2×Dic73 | C4×C8 | semidirect |
| 149. #10596833 | #99 | semidirect |
| 190. C73 | C8×#99 | semidirect |
| 285. C22⋊C4 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989614 | 2 |
| C22⋊C4×#10596833 | 2 |
| #22625169 | 2 |
| #22624774 | 2 |
| #22609718 | 2 |
| C8×#99 | 73 |