Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
484 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22596612 | C2 | semidirect |
| 4. #22586222 | C2 | semidirect |
| 5. C71×#1295 | C2 | semidirect |
| 25. #14556125 | Q8 | semidirect |
| 147. #1295 | D71 | semidirect |
| 148. C71 | #10358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596612 | 2 |
| #22589164 | 2 |
| #22589163 | 2 |
| #22586222 | 2 |
| C71×#1295 | 2 |
| #10358 | 71 |