Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
186 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22590586 | C2 | semidirect |
| 4. #22586408 | C2 | semidirect |
| 5. #22586402 | C2 | semidirect |
| 6. #22586378 | C2 | semidirect |
| 100. C71 | #12466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590586 | 2 |
| #22590516 | 2 |
| #22590421 | 2 |
| #22586408 | 2 |
| #22586402 | 2 |
| #22586378 | 2 |
| C71×#2171 | 2 |
| #12466 | 71 |