Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
554 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22593707 | C2 | semidirect |
| 4. #22586770 | C2 | semidirect |
| 5. #22586734 | C2 | semidirect |
| 6. #22586198 | C2 | semidirect |
| 92. C2×Dic142 | SD16 | semidirect |
| 227. C71 | #9999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598367 | 2 |
| #22597808 | 2 |
| #22593707 | 2 |
| #22586770 | 2 |
| #22586734 | 2 |
| #22586198 | 2 |
| C71×#1517 | 2 |
| #9999 | 71 |