Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1066 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22599343 | C2 | semidirect |
| 2. #22598726 | C2 | semidirect |
| 3. #22587646 | C2 | semidirect |
| 4. #22586964 | C2 | semidirect |
| 5. #22586938 | C2 | semidirect |
| 7. #17986556 | C22 | semidirect |
| 8. #17986394 | C22 | semidirect |
| 9. #17986358 | C22 | semidirect |
| 10. #17986358 | C22 | semidirect |
| 15. #17986056 | C22 | semidirect |
| 18. C4×#11765849 | C22 | semidirect |
| 19. #17985739 | C22 | semidirect |
| 20. #17985739 | C22 | semidirect |
| 33. #14556128 | C23 | semidirect |
| 44. #14556039 | C23 | semidirect |
| 45. #14556039 | C23 | semidirect |
| 189. C71 | #18997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599343 | 2 |
| #22598726 | 2 |
| #22587646 | 2 |
| #22586964 | 2 |
| #22586938 | 2 |
| C2×H(3,𝔽4)×C71 | 2 |
| #18997 | 71 |