Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
358 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×C4⋊(C71⋊C16) | C2 | semidirect |
| 3. #22586396 | C2 | semidirect |
| 4. #22586385 | C2 | semidirect |
| 5. C71×#1567 | C2 | semidirect |
| 132. #1567 | D71 | semidirect |
| 135. C71 | #11981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598919 | 2 |
| C2×C4⋊(C71⋊C16) | 2 |
| #22586396 | 2 |
| #22586385 | 2 |
| C71×#1567 | 2 |
| #11981 | 71 |