Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
394 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22589184 | C2 | semidirect |
| 3. #22587128 | C2 | semidirect |
| 5. #22587022 | C2 | semidirect |
| 7. C71×#1299 | C2 | semidirect |
| 165. #1299 | D71 | semidirect |
| 166. C71 | #10489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599267 | 2 |
| #22589184 | 2 |
| #22587128 | 2 |
| #22587073 | 2 |
| #22587022 | 2 |
| #22586758 | 2 |
| C71×#1299 | 2 |
| #10489 | 71 |