Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
374 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #22587115 | C2 | semidirect |
| 4. #22587112 | C2 | semidirect |
| 6. #22586237 | C2 | semidirect |
| 7. C71×#1301 | C2 | semidirect |
| 168. #1301 | D71 | semidirect |
| 169. C71 | #8863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596977 | 2 |
| #22588321 | 2 |
| #22587115 | 2 |
| #22587112 | 2 |
| #22586652 | 2 |
| #22586237 | 2 |
| C71×#1301 | 2 |
| #8863 | 71 |