Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
478 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 478 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 |
|---|---|---|
| 1. #22597424 | C2 | semidirect |
| 3. C4×#14556046 | C2 | semidirect |
| 5. #22586206 | C2 | semidirect |
| 6. #22586205 | C2 | semidirect |
| 218. C71 | #9188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597424 | 2 |
| #22594201 | 2 |
| C4×#14556046 | 2 |
| #22586938 | 2 |
| #22586206 | 2 |
| #22586205 | 2 |
| C71×#1527 | 2 |
| #9188 | 71 |