Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 39. #14556525 | C8 | semidirect |
| 40. #14556524 | C8 | semidirect |
| 41. #107×C73 | C8 | semidirect |
| 106. C8×C73 | C4⋊C8 | semidirect |
| 107. #10596831 | C4⋊C8 | semidirect |
| 141. C73 | #9594 | semidirect |
| 167. #107 | #10596842 | semidirect |
| 243. C8 | C4⋊#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627080 | 2 |
| C2×#17989677 | 2 |
| C2×C8×#10596842 | 2 |
| #22626939 | 2 |
| #107×#64408 | 2 |
| #9594 | 73 |