Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
364 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22596101 | C2 | semidirect |
| 5. #22586369 | C2 | semidirect |
| 6. #22586283 | C2 | semidirect |
| 7. C71×#1346 | C2 | semidirect |
| 178. #1346 | D71 | semidirect |
| 180. C71 | #12143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596101 | 2 |
| #22589570 | 2 |
| #22587342 | 2 |
| #22587311 | 2 |
| #22586369 | 2 |
| #22586283 | 2 |
| C71×#1346 | 2 |
| #12143 | 71 |