Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
454 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22596716 | C2 | semidirect |
| 5. #22586200 | C2 | semidirect |
| 6. #22586172 | C2 | semidirect |
| 7. C71×#1286 | C2 | semidirect |
| 25. #14556128 | Q8 | semidirect |
| 28. #14556125 | Q8 | semidirect |
| 176. #1286 | D71 | semidirect |
| 178. C71 | #10362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596716 | 2 |
| #22589167 | 2 |
| #22586901 | 2 |
| #22586899 | 2 |
| #22586200 | 2 |
| #22586172 | 2 |
| C71×#1286 | 2 |
| #10362 | 71 |