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. #22590657 | C2 | semidirect |
| 3. C2×Dic1136 | C2 | semidirect |
| 4. #22590466 | C2 | semidirect |
| 5. #22586532 | C2 | semidirect |
| 6. #22586481 | C2 | semidirect |
| 7. C71×#1417 | C2 | semidirect |
| 122. #1417 | 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 |
| #22590657 | 2 |
| C2×Dic1136 | 2 |
| #22590466 | 2 |
| #22586532 | 2 |
| #22586481 | 2 |
| C71×#1417 | 2 |
| #13672 | 71 |