Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
262 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #22586414 | C2 | semidirect |
| 4. #22586413 | C2 | semidirect |
| 5. C71×#1372 | C2 | semidirect |
| 24. C16×D71 | C8 | semidirect |
| 48. C71⋊C16 | C2×C8 | semidirect |
| 54. C16×C71 | C2×C8 | semidirect |
| 88. D71 | #1372 | direct (N × H) |
| 93. #1372 | D71 | direct (N × H) |
| 94. C71 | C2×#1372 | semidirect |
| 143. C16 | C8×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D71 | 2 |
| #335×D71 | 2 |
| #22586414 | 2 |
| #22586413 | 2 |
| C71×#1372 | 2 |
| C2×#1372 | 71 |