Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
394 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 394 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×#17985829 | C2 | semidirect |
| 4. #22586433 | C2 | semidirect |
| 5. C2×#368×C71 | C2 | semidirect |
| 104. C2×D71 | #368 | semidirect |
| 118. C2×#368 | D71 | semidirect |
| 121. C71 | #12837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D71 | 2 |
| C2×#17985829 | 2 |
| #22588375 | 2 |
| #22586433 | 2 |
| C2×#368×C71 | 2 |
| #12837 | 71 |