Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
596 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 596 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. #22588193 | C2 | semidirect |
| 3. C2×#17985738 | C2 | semidirect |
| 4. C71×#1745 | C2 | semidirect |
| 48. #97×C71 | D4 | semidirect |
| 164. #1745 | D71 | semidirect |
| 166. C71 | #9689 | semidirect |
| 210. #97 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596697 | 2 |
| #22588193 | 2 |
| C2×#17985738 | 2 |
| C71×#1745 | 2 |
| #9689 | 71 |