Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22597059 | C2 | semidirect |
| 3. #22587008 | C2 | semidirect |
| 4. #22586899 | C2 | semidirect |
| 5. #22586198 | C2 | semidirect |
| 6. #22586171 | C2 | semidirect |
| 7. C71×#1961 | C2 | semidirect |
| 10. #17986375 | C4 | semidirect |
| 11. #17986345 | C4 | semidirect |
| 112. C2×C8×C71 | D8 | semidirect |
| 198. #1961 | D71 | semidirect |
| 203. C71 | #9293 | semidirect |
| 304. C2×C8 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599258 | 2 |
| #22597059 | 2 |
| #22587008 | 2 |
| #22586899 | 2 |
| #22586198 | 2 |
| #22586171 | 2 |
| C71×#1961 | 2 |
| #9293 | 71 |