Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 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. #22587099 | C2 | semidirect |
| 4. #22587030 | C2 | semidirect |
| 6. #22586214 | C2 | semidirect |
| 7. C71×#1493 | C2 | semidirect |
| 186. #1493 | D71 | semidirect |
| 189. C71 | #10461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598133 | 2 |
| #22588329 | 2 |
| #22587099 | 2 |
| #22587030 | 2 |
| C2×#17985728 | 2 |
| #22586214 | 2 |
| C71×#1493 | 2 |
| #10461 | 71 |