Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22589326 | C2 | semidirect |
| 4. #22588764 | C2 | semidirect |
| 5. #22588517 | C2 | semidirect |
| 6. #22586208 | C2 | semidirect |
| 101. C22⋊Dic71 | SD16 | semidirect |
| 258. C71 | #10565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589326 | 2 |
| #22589177 | 2 |
| #22588769 | 2 |
| #22588764 | 2 |
| #22588517 | 2 |
| #22586208 | 2 |
| C71×#3187 | 2 |
| #10565 | 71 |