Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22589115 | C2 | semidirect |
| 2. #22587025 | C2 | semidirect |
| 4. C2×#17985748 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 178. C71 | #10551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589115 | 2 |
| #22587025 | 2 |
| #22587017 | 2 |
| C2×#17985748 | 2 |
| #22586739 | 2 |
| #22586191 | 2 |
| C71×#3141 | 2 |
| #10551 | 71 |