Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1056 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22599465 | C2 | semidirect |
| 2. #22598800 | C2 | semidirect |
| 3. #22587485 | C2 | semidirect |
| 4. #22587456 | C2 | semidirect |
| 5. #22587002 | C2 | semidirect |
| 6. #22586757 | C2 | semidirect |
| 9. C2×#14556128 | C22 | semidirect |
| 12. #17986378 | C22 | semidirect |
| 16. #17986289 | C22 | semidirect |
| 17. #17986052 | C22 | semidirect |
| 18. C4×#11765849 | C22 | semidirect |
| 19. #17985748 | C22 | semidirect |
| 21. D4⋊(C71⋊C8) | C22 | semidirect |
| 179. C71 | #18715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599465 | 2 |
| #22598800 | 2 |
| #22587485 | 2 |
| #22587456 | 2 |
| #22587002 | 2 |
| #22586757 | 2 |
| C71×#3549 | 2 |
| #18715 | 71 |