Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22588493 | C2 | semidirect |
| 3. #22587116 | C2 | semidirect |
| 6. #22586168 | C2 | semidirect |
| 7. C71×#1571 | C2 | semidirect |
| 133. #1571 | D71 | semidirect |
| 137. C71 | #10667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589171 | 2 |
| #22588493 | 2 |
| #22587116 | 2 |
| #22586740 | 2 |
| #22586738 | 2 |
| #22586168 | 2 |
| C71×#1571 | 2 |
| #10667 | 71 |