Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 2. #22588477 | C2 | semidirect |
| 3. #22587129 | C2 | semidirect |
| 6. #22586178 | C2 | semidirect |
| 7. C71×#1299 | C2 | semidirect |
| 172. #1299 | D71 | semidirect |
| 174. C71 | #8900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597466 | 2 |
| #22588477 | 2 |
| #22587129 | 2 |
| #22586780 | 2 |
| #22586720 | 2 |
| #22586178 | 2 |
| C71×#1299 | 2 |
| #8900 | 71 |