Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22591063 | C2 | semidirect |
| 3. #22589171 | C2 | semidirect |
| 4. #22587009 | C2 | semidirect |
| 5. #22586899 | C2 | semidirect |
| 6. #22586168 | C2 | semidirect |
| 7. C71×#1286 | C2 | semidirect |
| 11. #17986376 | C4 | semidirect |
| 12. #17986346 | C4 | semidirect |
| 33. #14556128 | C2×C4 | semidirect |
| 37. #14556125 | C2×C4 | semidirect |
| 66. C4×C8×C71 | C2×C4 | semidirect |
| 109. C4×Dic71 | D8 | semidirect |
| 217. #1286 | D71 | semidirect |
| 219. C71 | #9299 | semidirect |
| 276. C4×C8 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599260 | 2 |
| #22591063 | 2 |
| #22589171 | 2 |
| #22587009 | 2 |
| #22586899 | 2 |
| #22586168 | 2 |
| C71×#1286 | 2 |
| #9299 | 71 |