Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #22586514 | C2 | semidirect |
| 4. #22586499 | C2 | semidirect |
| 6. #17986611 | C4 | semidirect |
| 8. #17986371 | C4 | semidirect |
| 9. #17986363 | C4 | semidirect |
| 15. #17986060 | C4 | semidirect |
| 28. #14556128 | C2×C4 | semidirect |
| 30. #14556120 | C2×C4 | semidirect |
| 42. #14556039 | C2×C4 | semidirect |
| 43. C4×C71⋊C8 | C2×C4 | semidirect |
| 158. C71 | #13607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599412 | 2 |
| #22590032 | 2 |
| #22586514 | 2 |
| #22586499 | 2 |
| C71×#2127 | 2 |
| #13607 | 71 |