Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
326 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×#17985829 | C2 | semidirect |
| 3. #22586531 | C2 | direct (N × H) |
| 4. C2×M64×C71 | C2 | semidirect |
| 14. #17985829 | C22 | semidirect |
| 17. M64×C71 | C22 | semidirect |
| 101. C2×C71 | #1419 | semidirect |
| 105. C2×M64 | D71 | semidirect |
| 108. C71 | C2×#1419 | semidirect |
| 119. M64 | C2×D71 | semidirect |
| 205. C2 | #22586531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1136 | 2 |
| C2×#17985829 | 2 |
| #22586531 | 2 |
| C2×M64×C71 | 2 |
| C2×#1419 | 71 |