Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 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. #22590585 | C2 | semidirect |
| 4. #22586407 | C2 | semidirect |
| 5. #22586400 | C2 | semidirect |
| 6. #22586379 | 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 |
|---|---|
| #22590585 | 2 |
| #22590516 | 2 |
| #22590182 | 2 |
| #22586407 | 2 |
| #22586400 | 2 |
| #22586379 | 2 |
| C71×#2214 | 2 |
| #12466 | 71 |