Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
850 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 167 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×#17985742 | C2 | semidirect |
| 4. C71×#1831 | C2 | semidirect |
| 31. C4⋊(C71⋊C8) | D4 | semidirect |
| 128. #1831 | D71 | semidirect |
| 131. C71 | #9706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596735 | 2 |
| #22588193 | 2 |
| C2×#17985742 | 2 |
| C71×#1831 | 2 |
| #9706 | 71 |