Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 13. #17989428 | C4 | semidirect |
| 14. #17989428 | C4 | semidirect |
| 17. #17988340 | C4 | semidirect |
| 18. #17988339 | C4 | semidirect |
| 19. #335×C73 | C4 | semidirect |
| 24. #14556659 | C8 | semidirect |
| 88. C8×C73 | C4×C8 | semidirect |
| 91. #10596831 | C4×C8 | semidirect |
| 115. C73 | #8285 | semidirect |
| 127. #335 | #64408 | semidirect |
| 201. C8 | C8×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556659 | 2 |
| #22625724 | 2 |
| #22625125 | 2 |
| #22624765 | 2 |
| #335×D73 | 2 |
| #8285 | 73 |