Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
554 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22596317 | C2 | semidirect |
| 2. #22589428 | C2 | semidirect |
| 4. #22586165 | C2 | semidirect |
| 5. #22586163 | C2 | semidirect |
| 6. #22586160 | C2 | semidirect |
| 7. C71×#2041 | C2 | semidirect |
| 233. #2041 | D71 | semidirect |
| 239. C71 | #7746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596317 | 2 |
| #22589428 | 2 |
| #22589411 | 2 |
| #22586165 | 2 |
| #22586163 | 2 |
| #22586160 | 2 |
| C71×#2041 | 2 |
| #7746 | 71 |