Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
602 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22589180 | C2 | semidirect |
| 3. #22587095 | C2 | semidirect |
| 4. #22587009 | C2 | semidirect |
| 5. #22587008 | C2 | semidirect |
| 6. #22586627 | C2 | semidirect |
| 7. C71×#1965 | C2 | semidirect |
| 142. C71⋊C8 | #100 | semidirect |
| 171. #1965 | D71 | semidirect |
| 176. C71 | #9811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986375 | 2 |
| #22589180 | 2 |
| #22587095 | 2 |
| #22587009 | 2 |
| #22587008 | 2 |
| #22586627 | 2 |
| C71×#1965 | 2 |
| #9811 | 71 |