Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22587099 | C2 | semidirect |
| 4. #22586791 | C2 | semidirect |
| 14. #500×C71 | C4 | semidirect |
| 15. #493×C71 | C4 | semidirect |
| 16. #486×C71 | C4 | semidirect |
| 54. C4×Dic71 | D8 | semidirect |
| 132. C71 | #9847 | semidirect |
| 134. #500 | Dic71 | semidirect |
| 135. #493 | Dic71 | semidirect |
| 136. #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 |
| #22587099 | 2 |
| #22586791 | 2 |
| C71×#3169 | 2 |
| #9847 | 71 |