Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
354 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22590138 | C2 | semidirect |
| 3. #335×D71 | C2 | semidirect |
| 4. #22586396 | C2 | semidirect |
| 5. #22586394 | C2 | semidirect |
| 6. #22586386 | C2 | semidirect |
| 7. C71×#1361 | C2 | semidirect |
| 144. #1361 | D71 | semidirect |
| 145. C71 | #11947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598917 | 2 |
| #22590138 | 2 |
| #335×D71 | 2 |
| #22586396 | 2 |
| #22586394 | 2 |
| #22586386 | 2 |
| C71×#1361 | 2 |
| #11947 | 71 |