Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
318 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 16. #17985814 | C4 | semidirect |
| 136. C71 | #13139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985823 | 2 |
| C2×#17985814 | 2 |
| #22589211 | 2 |
| #22586440 | 2 |
| #22586424 | 2 |
| C71×#1778 | 2 |
| #13139 | 71 |