Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
298 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 89. C8×C73 | #108 | semidirect |
| 118. C73 | #9624 | semidirect |
| 205. C8 | #14556662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626045 | 2 |
| #22625489 | 2 |
| C8×#11924038 | 2 |
| #22624823 | 2 |
| #335×D73 | 2 |
| #9624 | 73 |