Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
392 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22587038 | C2 | semidirect |
| 4. #22586840 | C2 | semidirect |
| 6. #22586197 | C2 | semidirect |
| 7. C71×#1573 | C2 | semidirect |
| 186. #1573 | D71 | semidirect |
| 191. C71 | #10510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599345 | 2 |
| #22589270 | 2 |
| #22587038 | 2 |
| #22586840 | 2 |
| #22586691 | 2 |
| #22586197 | 2 |
| C71×#1573 | 2 |
| #10510 | 71 |