Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
498 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. #22589169 | C2 | semidirect |
| 2. #22588085 | C2 | semidirect |
| 3. #22587096 | C2 | semidirect |
| 4. #22586791 | C2 | semidirect |
| 14. #500×C71 | C4 | semidirect |
| 15. #493×C71 | C4 | semidirect |
| 16. #486×C71 | C4 | semidirect |
| 129. C71 | #9852 | semidirect |
| 131. #500 | Dic71 | semidirect |
| 132. #493 | Dic71 | semidirect |
| 133. #486 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589169 | 2 |
| #22588085 | 2 |
| #22587096 | 2 |
| #22586791 | 2 |
| C71×#3169 | 2 |
| #9852 | 71 |