Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
394 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#17985829 | C2 | semidirect |
| 3. #22586434 | C2 | semidirect |
| 73. C22×C71 | #368 | semidirect |
| 89. C71 | #12837 | semidirect |
| 158. C22 | #17985829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985829 | 2 |
| #22588378 | 2 |
| #22586434 | 2 |
| C23×C16×C71 | 2 |
| #12837 | 71 |