Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
214 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22586538 | C2 | semidirect |
| 4. #22586537 | C2 | semidirect |
| 5. C71×#1422 | C2 | semidirect |
| 87. D71 | #1422 | direct (N × H) |
| 92. #1422 | D71 | direct (N × H) |
| 93. C71 | C2×#1422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D71 | 2 |
| C4×C16×D71 | 2 |
| #22586538 | 2 |
| #22586537 | 2 |
| C71×#1422 | 2 |
| C2×#1422 | 71 |