Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 10. #17989476 | C4 | semidirect |
| 11. C4×#11924031 | C4 | semidirect |
| 14. #17988362 | C4 | semidirect |
| 15. C4×#11924003 | C4 | semidirect |
| 16. C4×C16×C73 | C4 | semidirect |
| 101. C73 | #12594 | semidirect |
| 113. C4×C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556666 | 2 |
| C4×#14556645 | 2 |
| #22624971 | 2 |
| C4×#14556530 | 2 |
| #12594 | 73 |