Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
344 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22586356 | C2 | semidirect |
| 5. #22586355 | C2 | semidirect |
| 6. #22586354 | C2 | semidirect |
| 7. C71×#1349 | C2 | semidirect |
| 165. #1349 | D71 | semidirect |
| 166. C71 | #11864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598914 | 2 |
| #22590140 | 2 |
| #22588476 | 2 |
| #22586356 | 2 |
| #22586355 | 2 |
| #22586354 | 2 |
| C71×#1349 | 2 |
| #11864 | 71 |