Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22590140 | C2 | semidirect |
| 3. #22588476 | C2 | semidirect |
| 4. #22586358 | C2 | semidirect |
| 7. C71×#1350 | C2 | semidirect |
| 154. #1350 | D71 | semidirect |
| 157. C71 | #11866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598911 | 2 |
| #22590140 | 2 |
| #22588476 | 2 |
| #22586358 | 2 |
| #22586356 | 2 |
| #22586354 | 2 |
| C71×#1350 | 2 |
| #11866 | 71 |