Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22590134 | C2 | semidirect |
| 4. #22586451 | C2 | semidirect |
| 119. C71 | #12924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590134 | 2 |
| C2×#17985781 | 2 |
| #22588382 | 2 |
| #22586451 | 2 |
| C2×#430×C71 | 2 |
| #12924 | 71 |