Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
942 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. #22602740 | C2 | semidirect |
| 2. #22599331 | C2 | semidirect |
| 3. #22587661 | C2 | semidirect |
| 4. #22587632 | C2 | semidirect |
| 5. #22586978 | C2 | semidirect |
| 6. #22586950 | C2 | semidirect |
| 7. C71×#3135 | C2 | semidirect |
| 165. #3135 | D71 | semidirect |
| 170. C71 | #19061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602740 | 2 |
| #22599331 | 2 |
| #22587661 | 2 |
| #22587632 | 2 |
| #22586978 | 2 |
| #22586950 | 2 |
| C71×#3135 | 2 |
| #19061 | 71 |