Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22588514 | C2 | semidirect |
| 3. #22587105 | C2 | semidirect |
| 5. #22586240 | C2 | semidirect |
| 6. #22586231 | C2 | semidirect |
| 176. C71 | #8916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597510 | 2 |
| #22588514 | 2 |
| #22587105 | 2 |
| #22586928 | 2 |
| #22586240 | 2 |
| #22586231 | 2 |
| C71×#1495 | 2 |
| #8916 | 71 |