Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22586545 | C2 | semidirect |
| 3. #22586538 | C2 | semidirect |
| 5. C71×#2253 | C2 | semidirect |
| 67. #2253 | D71 | semidirect |
| 72. C71 | #13709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590222 | 2 |
| #22586545 | 2 |
| #22586538 | 2 |
| #22586526 | 2 |
| C71×#2253 | 2 |
| #13709 | 71 |