Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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×#17985839 | C2 | semidirect |
| 3. #22590462 | C2 | semidirect |
| 4. #22586534 | C2 | semidirect |
| 5. #22586524 | C2 | semidirect |
| 6. #22586483 | C2 | semidirect |
| 7. C71×#2264 | C2 | semidirect |
| 118. #2264 | D71 | semidirect |
| 124. C71 | #13672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601490 | 2 |
| C2×#17985839 | 2 |
| #22590462 | 2 |
| #22586534 | 2 |
| #22586524 | 2 |
| #22586483 | 2 |
| C71×#2264 | 2 |
| #13672 | 71 |