Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
368 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 29. #14556498 | C8 | semidirect |
| 30. #95×C73 | C8 | semidirect |
| 171. C73 | #7122 | semidirect |
| 198. #95 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626940 | 2 |
| #22625117 | 2 |
| #7122 | 73 |