Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22590217 | C2 | semidirect |
| 3. #22586547 | C2 | semidirect |
| 4. #22586529 | C2 | semidirect |
| 5. #22586527 | C2 | semidirect |
| 6. #22586476 | C2 | semidirect |
| 7. C71×#2179 | C2 | semidirect |
| 10. #17985836 | C4 | semidirect |
| 11. #17985834 | C4 | semidirect |
| 28. C71⋊C32 | C2×C4 | semidirect |
| 31. Q32×C71 | C2×C4 | semidirect |
| 33. D16×C71 | C2×C4 | semidirect |
| 89. #2179 | D71 | semidirect |
| 95. C71 | #13658 | semidirect |
| 113. Q32 | C4×D71 | semidirect |
| 117. D16 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590652 | 2 |
| #22590217 | 2 |
| #22586547 | 2 |
| #22586529 | 2 |
| #22586527 | 2 |
| #22586476 | 2 |
| C71×#2179 | 2 |
| #13658 | 71 |