Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1066 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. #22599345 | C2 | semidirect |
| 3. #22598726 | C2 | semidirect |
| 4. #22587648 | C2 | semidirect |
| 5. #22586939 | C2 | semidirect |
| 6. C71×#1533 | C2 | semidirect |
| 10. #17986556 | C22 | semidirect |
| 16. #17986393 | C22 | semidirect |
| 17. #17986359 | C22 | semidirect |
| 18. #17986358 | C22 | semidirect |
| 25. C4×#11765849 | C22 | semidirect |
| 26. #17985738 | C22 | semidirect |
| 28. #432×C71 | C22 | semidirect |
| 29. #329×C71 | C22 | semidirect |
| 38. #14556128 | C23 | semidirect |
| 64. #14556039 | C23 | semidirect |
| 75. #97×C71 | C23 | semidirect |
| 187. #1533 | D71 | semidirect |
| 189. C71 | #18997 | semidirect |
| 207. #432 | C2×D71 | semidirect |
| 212. #329 | C2×D71 | semidirect |
| 257. #97 | C22×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986741 | 2 |
| #22599345 | 2 |
| #22598726 | 2 |
| #22587648 | 2 |
| #22586939 | 2 |
| C71×#1533 | 2 |
| #18997 | 71 |