Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
314 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22600945 | C2 | semidirect |
| 2. #22590582 | C2 | semidirect |
| 3. #22590376 | C2 | semidirect |
| 4. #22587819 | C2 | semidirect |
| 5. #22586391 | C2 | semidirect |
| 6. #22586308 | C2 | semidirect |
| 7. C71×#1330 | C2 | semidirect |
| 159. #1330 | D71 | semidirect |
| 160. C71 | #12348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600945 | 2 |
| #22590582 | 2 |
| #22590376 | 2 |
| #22587819 | 2 |
| #22586391 | 2 |
| #22586308 | 2 |
| C71×#1330 | 2 |
| #12348 | 71 |