Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
502 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 502 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 |
|---|---|---|
| 2. #22589113 | C2 | semidirect |
| 3. #22587009 | C2 | semidirect |
| 4. C2×#17985742 | C2 | semidirect |
| 5. #22586739 | C2 | semidirect |
| 6. #22586190 | C2 | semidirect |
| 7. C71×#1547 | C2 | semidirect |
| 202. #1547 | D71 | semidirect |
| 207. C71 | #10549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598793 | 2 |
| #22589113 | 2 |
| #22587009 | 2 |
| C2×#17985742 | 2 |
| #22586739 | 2 |
| #22586190 | 2 |
| C71×#1547 | 2 |
| #10549 | 71 |