Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22590141 | C2 | semidirect |
| 3. #22587094 | C2 | semidirect |
| 4. #22586308 | C2 | semidirect |
| 5. #22586307 | C2 | semidirect |
| 6. #22586306 | C2 | semidirect |
| 7. C71×#1333 | C2 | semidirect |
| 21. #17985775 | C22 | semidirect |
| 22. #17985750 | C22 | semidirect |
| 25. #346×C71 | C22 | semidirect |
| 26. #334×C71 | C22 | semidirect |
| 76. D568 | M16 | semidirect |
| 97. D8×C71 | M16 | semidirect |
| 173. #1333 | D71 | semidirect |
| 174. C71 | #11663 | semidirect |
| 190. #346 | C2×D71 | semidirect |
| 193. #334 | C2×D71 | semidirect |
| 248. D8 | #11765848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D71 | 2 |
| #22590141 | 2 |
| #22587094 | 2 |
| #22586308 | 2 |
| #22586307 | 2 |
| #22586306 | 2 |
| C71×#1333 | 2 |
| #11663 | 71 |