Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
460 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22588333 | C2 | semidirect |
| 5. #22586734 | C2 | semidirect |
| 6. #22586237 | C2 | semidirect |
| 7. C71×#1571 | C2 | semidirect |
| 176. #1571 | D71 | semidirect |
| 181. C71 | #10442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986200 | 2 |
| #22588333 | 2 |
| #22587009 | 2 |
| #22587007 | 2 |
| #22586734 | 2 |
| #22586237 | 2 |
| C71×#1571 | 2 |
| #10442 | 71 |