Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
378 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 30. #14556502 | C8 | semidirect |
| 31. #14556501 | C8 | semidirect |
| 32. #97×C73 | C8 | semidirect |
| 106. C73 | #8786 | semidirect |
| 132. #97 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627075 | 2 |
| #22627073 | 2 |
| #22626937 | 2 |
| #97×#64408 | 2 |
| #8786 | 73 |