Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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. #22626270 | C2 | semidirect |
| 3. #22625866 | C2 | semidirect |
| 4. #22624997 | C2 | semidirect |
| 16. #17988705 | C4 | semidirect |
| 17. #17988704 | C4 | semidirect |
| 18. #17988703 | C4 | semidirect |
| 24. #443×C73 | C4 | semidirect |
| 83. Dic292 | C4⋊C4 | semidirect |
| 88. D584 | C4⋊C4 | semidirect |
| 112. Q16×C73 | C4⋊C4 | semidirect |
| 114. D8×C73 | C4⋊C4 | semidirect |
| 187. C73 | #12823 | semidirect |
| 196. #443 | #64408 | semidirect |
| 264. Q16 | C4⋊#64408 | semidirect |
| 271. D8 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626270 | 2 |
| D73⋊#360 | 2 |
| #22625866 | 2 |
| #22624997 | 2 |
| #443×D73 | 2 |
| #12823 | 73 |