Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
528 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 528 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 |
|---|---|---|
| 1. C2×#17989597 | C2 | semidirect |
| 2. C2×#17989504 | C2 | semidirect |
| 3. #22626159 | C2 | semidirect |
| 4. #22625002 | C2 | semidirect |
| 17. #17988825 | C4 | semidirect |
| 18. #17988824 | C4 | semidirect |
| 19. #17988823 | C4 | semidirect |
| 24. #467×C73 | C4 | semidirect |
| 35. #14556659 | D4 | semidirect |
| 205. C73 | #13002 | semidirect |
| 212. #467 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989597 | 2 |
| C2×#17989504 | 2 |
| #22626159 | 2 |
| #22625002 | 2 |
| #22619514 | 2 |
| #13002 | 73 |