Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 24. #14556646 | C8 | semidirect |
| 29. #14556502 | C8 | semidirect |
| 30. #14556501 | C8 | semidirect |
| 31. #97×C73 | C8 | semidirect |
| 99. C73 | #8132 | semidirect |
| 122. #97 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627065 | 2 |
| C42×#10596842 | 2 |
| (C2×#10596842)⋊C8 | 2 |
| #97×#64408 | 2 |
| #8132 | 73 |