Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 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 |
|---|---|---|
| 1. #22590660 | C2 | semidirect |
| 3. #22590601 | C2 | semidirect |
| 4. #22590222 | C2 | semidirect |
| 5. #22586534 | C2 | semidirect |
| 6. #22586531 | C2 | semidirect |
| 7. C71×#1422 | C2 | semidirect |
| 101. #1422 | D71 | semidirect |
| 104. C71 | #13691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590660 | 2 |
| #22590655 | 2 |
| #22590601 | 2 |
| #22590222 | 2 |
| #22586534 | 2 |
| #22586531 | 2 |
| C71×#1422 | 2 |
| #13691 | 71 |