Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
150 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 34 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. #22625047 | C2 | semidirect |
| 2. #22624999 | C2 | semidirect |
| 6. C2×D1168 | C4 | semidirect |
| 10. #367×C73 | C4 | semidirect |
| 73. C73 | #7422 | semidirect |
| 79. #367 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625047 | 2 |
| #22624999 | 2 |
| #22612035 | 2 |
| #7422 | 73 |