Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1026 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22589139 | C2 | semidirect |
| 2. #22587035 | C2 | semidirect |
| 3. #22586951 | C2 | semidirect |
| 4. #22586681 | C2 | semidirect |
| 6. #17986056 | C22 | semidirect |
| 7. C2×C4⋊(C71⋊C8) | C22 | semidirect |
| 9. C2×#14556039 | C22 | semidirect |
| 174. C71 | #8456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589139 | 2 |
| #22587035 | 2 |
| #22586951 | 2 |
| #22586681 | 2 |
| C71×#3496 | 2 |
| #8456 | 71 |