Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 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. #22591065 | C2 | semidirect |
| 3. #22587009 | C2 | semidirect |
| 4. #22586900 | C2 | semidirect |
| 5. #22586200 | C2 | semidirect |
| 6. #22586169 | C2 | semidirect |
| 7. C71×#1963 | C2 | semidirect |
| 10. #17986375 | C4 | semidirect |
| 11. #17986347 | C4 | semidirect |
| 48. C4×C71⋊C8 | C2×C4 | semidirect |
| 53. C4⋊Q8×C71 | C2×C4 | semidirect |
| 54. #127×C71 | C2×C4 | semidirect |
| 119. C42×C71 | D8 | semidirect |
| 214. #1963 | D71 | semidirect |
| 219. C71 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D71 | semidirect |
| 251. #127 | C4×D71 | semidirect |
| 331. C42 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599255 | 2 |
| #22591065 | 2 |
| #22587009 | 2 |
| #22586900 | 2 |
| #22586200 | 2 |
| #22586169 | 2 |
| C71×#1963 | 2 |
| #9299 | 71 |