Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
290 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22590376 | C2 | semidirect |
| 2. #22590372 | C2 | semidirect |
| 3. #22587954 | C2 | semidirect |
| 4. #22587134 | C2 | semidirect |
| 5. #22586409 | C2 | semidirect |
| 6. #22586385 | C2 | semidirect |
| 7. C71×#1361 | C2 | semidirect |
| 55. D568 | D8 | semidirect |
| 104. C71⋊C8 | D16 | semidirect |
| 134. #1361 | D71 | semidirect |
| 135. C71 | #12424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590376 | 2 |
| #22590372 | 2 |
| #22587954 | 2 |
| #22587134 | 2 |
| #22586409 | 2 |
| #22586385 | 2 |
| C71×#1361 | 2 |
| #12424 | 71 |