Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
608 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. #22627074 | C2 | semidirect |
| 2. #22626930 | C2 | semidirect |
| 28. #14556588 | C8 | semidirect |
| 30. #14556587 | C8 | semidirect |
| 32. #127×C73 | C8 | semidirect |
| 129. C73 | #7603 | semidirect |
| 147. #127 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627074 | 2 |
| #22626930 | 2 |
| #127×#64408 | 2 |
| #7603 | 73 |