Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
666 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. C2×#17985798 | C2 | semidirect |
| 3. #22588454 | C2 | semidirect |
| 167. C71 | #12730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590029 | 2 |
| C2×#17985798 | 2 |
| #22588454 | 2 |
| C71×#3509 | 2 |
| #12730 | 71 |