Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22590623 | C2 | semidirect |
| 3. #22587855 | C2 | semidirect |
| 4. #22586391 | C2 | semidirect |
| 5. #22586321 | C2 | semidirect |
| 84. D8×C71 | Q16 | semidirect |
| 143. C71 | #12414 | semidirect |
| 205. D8 | #11765855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601296 | 2 |
| #22590623 | 2 |
| #22587855 | 2 |
| #22586391 | 2 |
| #22586321 | 2 |
| #22586307 | 2 |
| C71×#2226 | 2 |
| #12414 | 71 |