Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
182 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22590210 | C2 | semidirect |
| 4. #22586532 | C2 | semidirect |
| 6. #22586475 | C2 | semidirect |
| 7. C71×#1426 | C2 | semidirect |
| 12. Dic1136 | C4 | semidirect |
| 13. #17985838 | C4 | semidirect |
| 87. #1426 | D71 | semidirect |
| 91. C71 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590660 | 2 |
| #22590225 | 2 |
| #22590210 | 2 |
| #22586532 | 2 |
| #22586526 | 2 |
| #22586475 | 2 |
| C71×#1426 | 2 |
| #13657 | 71 |