Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
288 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #22626988 | C2 | semidirect |
| 4. #22626987 | C2 | semidirect |
| 137. C73 | #11643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627133 | 2 |
| #22627132 | 2 |
| #22626988 | 2 |
| #22626987 | 2 |
| #22626719 | 2 |
| #11643 | 73 |