Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
826 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 136 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. C4×#14556648 | C2 | semidirect |
| 2. C2×#17989439 | C2 | semidirect |
| 3. #22625109 | C2 | semidirect |
| 12. C2×#14556588 | C4 | semidirect |
| 19. #17988488 | C4 | semidirect |
| 20. #384×C73 | C4 | semidirect |
| 27. #14556648 | D4 | semidirect |
| 207. C4×C73 | #327 | semidirect |
| 228. C73 | #9680 | semidirect |
| 240. #384 | #64408 | semidirect |
| 434. C4 | #17989439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556648 | 2 |
| C2×#17989439 | 2 |
| #22625109 | 2 |
| #22618277 | 2 |
| #9680 | 73 |