Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
288 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 68 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. #22626300 | C2 | semidirect |
| 2. #22624879 | C2 | semidirect |
| 107. C73 | #11524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626300 | 2 |
| #22624879 | 2 |
| #22624865 | 2 |
| #22618575 | 2 |
| #11524 | 73 |